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Add and Subtract Square Roots

Add and subtract like square roots

Add and Subtract Like Square Roots

Think about adding like terms with variables as you do the next few examples. When you have like radicands, you just add or subtract the coefficients. When the radicands are not like, you cannot combine the terms.

Example

Try it.

Simplify: \(2\sqrt{2}-7\sqrt{2}\).

Solution

\(2\sqrt{2}-7\sqrt{2}\)
Since the radicals are like, we subtract the coefficients.\(-5\sqrt{2}\)

Example

Try it.

Simplify: \(3\sqrt{y}+4\sqrt{y}\).

Solution

\(3\sqrt{y}+4\sqrt{y}\)
Since the radicals are like, we add the coefficients.\(7\sqrt{y}\)

Example

Try it.

Simplify: \(4\sqrt{x}-2\sqrt{y}\).

Solution

\(4\sqrt{x}-2\sqrt{y}\)
Since the radicals are not like, we cannot
subtract them. We leave the expression as is.		\(4\sqrt{x}-2\sqrt{y}\)

Example

Try it.

Simplify: \(5\sqrt{13}+4\sqrt{13}+2\sqrt{13}\).

Solution

\(5\sqrt{13}+4\sqrt{13}+2\sqrt{13}\)
Since the radicals are like, we add the coefficients.\(11\sqrt{13}\)

Example

Try it.

Simplify: \(2\sqrt{6}-6\sqrt{6}+3\sqrt{3}\).

Solution

\(2\sqrt{6}-6\sqrt{6}+3\sqrt{3}\)
Since the first two radicals are like, we
subtract their coefficients.		\(-4\sqrt{6}+3\sqrt{3}\)

Example

Try it.

Simplify: \(2\sqrt{5n}-6\sqrt{5n}+4\sqrt{5n}\).

Solution

\(2\sqrt{5n}-6\sqrt{5n}+4\sqrt{5n}\)
Since the radicals are like, we combine them.\(0\sqrt{5n}\)
Simplify.0

When radicals contain more than one variable, as long as all the variables and their exponents are identical, the radicals are like.

Example

Try it.

Simplify: \(\sqrt{3xy}+5\sqrt{3xy}-4\sqrt{3xy}\).

Solution

\(\sqrt{3xy}+5\sqrt{3xy}-4\sqrt{3xy}\)
Since the radicals are like, we combine them.\(2\sqrt{3xy}\)

Add and Subtract Square Roots that Need Simplification

Remember that we always simplify square roots by removing the largest perfect-square factor. Sometimes when we have to add or subtract square roots that do not appear to have like radicals, we find like radicals after simplifying the square roots.

Example

Try it.

Simplify: \(\sqrt{20}+3\sqrt{5}\).

Solution

\(\sqrt{20}+3\sqrt{5}\)
Simplify the radicals, when possible.\(\sqrt{4}\cdot \sqrt{5}+3\sqrt{5}\)
\(2\sqrt{5}+3\sqrt{5}\)
Combine the like radicals.\(5\sqrt{5}\)

Example

Try it.

Simplify: \(\sqrt{48}-\sqrt{75}\).

Solution

\(\sqrt{48}-\sqrt{75}\)
Simplify the radicals.\(\sqrt{16}\cdot \sqrt{3}-\sqrt{25}\cdot \sqrt{3}\)
\(4\sqrt{3}-5\sqrt{3}\)
Combine the like radicals.\(\text{-}\sqrt{3}\)

Just like we use the Associative Property of Multiplication to simplify \(5(3x)\) and get \(15x\), we can simplify \(5(3\sqrt{x})\) and get \(15\sqrt{x}\). We will use the Associative Property to do this in the next example.

Example

Try it.

Simplify: \(5\sqrt{18}-2\sqrt{8}\).

Solution

\(5\sqrt{18}-2\sqrt{8}\)
Simplify the radicals.\(5\cdot \sqrt{9}\cdot \sqrt{2}-2\cdot \sqrt{4}\cdot \sqrt{2}\)
\(5\cdot 3\cdot \sqrt{2}-2\cdot 2\cdot \sqrt{2}\)
\(15\sqrt{2}-4\sqrt{2}\)
Combine the like radicals.\(11\sqrt{2}\)

Example

Try it.

Simplify: \(\frac{3}{4}\sqrt{192}-\frac{5}{6}\sqrt{108}\).

Solution

\(\frac{3}{4}\sqrt{192}-\frac{5}{6}\sqrt{108}\)
Simplify the radicals.\(\frac{3}{4}\sqrt{64}\cdot \sqrt{3}-\frac{5}{6}\sqrt{36}\cdot \sqrt{3}\)
\(\frac{3}{4}\cdot 8\cdot \sqrt{3}-\frac{5}{6}\cdot 6\cdot \sqrt{3}\)
\(6\sqrt{3}-5\sqrt{3}\)
Combine the like radicals.\(\sqrt{3}\)

Example

Try it.

Simplify: \(\frac{2}{3}\sqrt{48}-\frac{3}{4}\sqrt{12}\).

Solution

\(\frac{2}{3}\sqrt{48}-\frac{3}{4}\sqrt{12}\)
Simplify the radicals.\(\frac{2}{3}\sqrt{16}\cdot \sqrt{3}-\frac{3}{4}\sqrt{4}\cdot \sqrt{3}\)
\(\frac{2}{3}\cdot 4\cdot \sqrt{3}-\frac{3}{4}\cdot 2\cdot \sqrt{3}\)
\(\frac{8}{3}\sqrt{3}-\frac{3}{2}\sqrt{3}\)
Find a common denominator to subtract the
coefficients of the like radicals.		\(\frac{16}{6}\sqrt{3}-\frac{9}{6}\sqrt{3}\)
Simplify.\(\frac{7}{6}\sqrt{3}\)

Condensed: the full section is in OpenStax Elementary Algebra 2e.

Key Concepts

  • To add or subtract like square roots, add or subtract the coefficients and keep the like square root.
  • Sometimes when we have to add or subtract square roots that do not appear to have like radicals, we find like radicals after simplifying the square roots.

Add and Subtract Square Roots

Add and Subtract Like Square Roots

In the following exercises, simplify.

Try it.

\(8\sqrt{2}-5\sqrt{2}\)

Solution

\(3\sqrt{2}\)

Try it.

\(7\sqrt{2}-3\sqrt{2}\)

Try it.

\(3\sqrt{5}+6\sqrt{5}\)

Solution

\(9\sqrt{5}\)

Try it.

\(4\sqrt{5}+8\sqrt{5}\)

Try it.

\(9\sqrt{7}-10\sqrt{7}\)

Solution

\(\text{-}\sqrt{7}\)

Try it.

\(11\sqrt{7}-12\sqrt{7}\)

Try it.

\(7\sqrt{y}+2\sqrt{y}\)

Solution

\(9\sqrt{y}\)

Try it.

\(9\sqrt{n}+3\sqrt{n}\)

Try it.

\(\sqrt{a}-4\sqrt{a}\)

Solution

\(-3\sqrt{a}\)

Try it.

\(\sqrt{b}-6\sqrt{b}\)

Try it.

\(5\sqrt{c}+2\sqrt{c}\)

Solution

\(7\sqrt{c}\)

Try it.

\(7\sqrt{d}+2\sqrt{d}\)

Try it.

\(8\sqrt{a}-2\sqrt{b}\)

Solution

\(8\sqrt{a}-2\sqrt{b}\)

Try it.

\(5\sqrt{c}-3\sqrt{d}\)

Try it.

\(5\sqrt{m}+\sqrt{n}\)

Solution

\(5\sqrt{m}+\sqrt{n}\)

Try it.

\(\sqrt{n}+3\sqrt{p}\)

Try it.

\(8\sqrt{7}+2\sqrt{7}+3\sqrt{7}\)

Solution

\(13\sqrt{7}\)

Try it.

\(6\sqrt{5}+3\sqrt{5}+\sqrt{5}\)

Try it.

\(3\sqrt{11}+2\sqrt{11}-8\sqrt{11}\)

Solution

\(-3\sqrt{11}\)

Try it.

\(2\sqrt{15}+5\sqrt{15}-9\sqrt{15}\)

Try it.

\(3\sqrt{3}-8\sqrt{3}+7\sqrt{5}\)

Solution

\(-5\sqrt{3}+7\sqrt{5}\)

Try it.

\(5\sqrt{7}-8\sqrt{7}+6\sqrt{3}\)

Try it.

\(6\sqrt{2}+2\sqrt{2}-3\sqrt{5}\)

Solution

\(8\sqrt{2}-3\sqrt{5}\)

Try it.

\(7\sqrt{5}+\sqrt{5}-8\sqrt{10}\)

Try it.

\(3\sqrt{2a}-4\sqrt{2a}+5\sqrt{2a}\)

Solution

\(4\sqrt{2a}\)

Try it.

\(\sqrt{11b}-5\sqrt{11b}+3\sqrt{11b}\)

Try it.

\(8\sqrt{3c}+2\sqrt{3c}-9\sqrt{3c}\)

Solution

\(\sqrt{3c}\)

Try it.

\(3\sqrt{5d}+8\sqrt{5d}-11\sqrt{5d}\)

Try it.

\(5\sqrt{3ab}+\sqrt{3ab}-2\sqrt{3ab}\)

Solution

\(4\sqrt{3ab}\)

Try it.

\(8\sqrt{11cd}+5\sqrt{11cd}-9\sqrt{11cd}\)

Try it.

\(2\sqrt{pq}-5\sqrt{pq}+4\sqrt{pq}\)

Solution

\(\sqrt{pq}\)

Try it.

\(11\sqrt{2rs}-9\sqrt{2rs}+3\sqrt{2rs}\)

Add and Subtract Square Roots that Need Simplification

In the following exercises, simplify.

Try it.

\(\sqrt{50}+4\sqrt{2}\)

Solution

\(9\sqrt{2}\)

Try it.

\(\sqrt{48}+2\sqrt{3}\)

Try it.

\(\sqrt{80}-3\sqrt{5}\)

Solution

\(\sqrt{5}\)

Try it.

\(\sqrt{28}-4\sqrt{7}\)

Try it.

\(\sqrt{27}-\sqrt{75}\)

Solution

\(-2\sqrt{3}\)

Try it.

\(\sqrt{72}-\sqrt{98}\)

Try it.

\(\sqrt{48}+\sqrt{27}\)

Solution

\(7\sqrt{3}\)

Try it.

\(\sqrt{45}+\sqrt{80}\)

Try it.

\(2\sqrt{50}-3\sqrt{72}\)

Solution

\(-8\sqrt{2}\)

Try it.

\(3\sqrt{98}-\sqrt{128}\)

Try it.

\(2\sqrt{12}+3\sqrt{48}\)

Solution

\(16\sqrt{3}\)

Try it.

\(4\sqrt{75}+2\sqrt{108}\)

Try it.

\(\frac{2}{3}\sqrt{72}+\frac{1}{5}\sqrt{50}\)

Solution

\(5\sqrt{2}\)

Try it.

\(\frac{2}{5}\sqrt{75}+\frac{3}{4}\sqrt{48}\)

Try it.

\(\frac{1}{2}\sqrt{20}-\frac{2}{3}\sqrt{45}\)

Solution

\(\text{-}\sqrt{5}\)

Try it.

\(\frac{2}{3}\sqrt{54}-\frac{3}{4}\sqrt{96}\)

Try it.

\(\frac{1}{6}\sqrt{27}-\frac{3}{8}\sqrt{48}\)

Solution

\(\text{-}\sqrt{3}\)

Try it.

\(\frac{1}{8}\sqrt{32}-\frac{1}{10}\sqrt{50}\)

Try it.

\(\frac{1}{4}\sqrt{98}-\frac{1}{3}\sqrt{128}\)

Solution

\(-\frac{11}{12}\sqrt{2}\)

Try it.

\(\frac{1}{3}\sqrt{24}+\frac{1}{4}\sqrt{54}\)

Try it.

\(\sqrt{72{a}^{5}}-\sqrt{50{a}^{5}}\)

Solution

\({a}^{2}\sqrt{2a}\)

Try it.

\(\sqrt{48{b}^{5}}-\sqrt{75{b}^{5}}\)

Try it.

\(\sqrt{80{c}^{7}}-\sqrt{20{c}^{7}}\)

Solution

\(2{c}^{3}\sqrt{5c}\)

Try it.

\(\sqrt{96{d}^{9}}-\sqrt{24{d}^{9}}\)

Try it.

\(9\sqrt{80{p}^{4}}-6\sqrt{98{p}^{4}}\)

Solution

\(36{p}^{2}\sqrt{5}-42{p}^{2}\sqrt{2}\)

Try it.

\(8\sqrt{72{q}^{6}}-3\sqrt{75{q}^{6}}\)

Try it.

\(2\sqrt{50{r}^{8}}+4\sqrt{54{r}^{8}}\)

Solution

\(10{r}^{4}\sqrt{2}+12{r}^{4}\sqrt{6}\)

Try it.

\(5\sqrt{27{s}^{6}}+2\sqrt{20{s}^{6}}\)

Try it.

\(3\sqrt{20{x}^{2}}-4\sqrt{45{x}^{2}}+5x\sqrt{80}\)

Solution

\(14x\sqrt{5}\)

Try it.

\(2\sqrt{28{x}^{2}}-\sqrt{63{x}^{2}}+6x\sqrt{7}\)

Try it.

\(3\sqrt{128{y}^{2}}+4y\sqrt{162}-8\sqrt{98{y}^{2}}\)

Solution

\(4y\sqrt{2}\)

Try it.

\(3\sqrt{75{y}^{2}}+8y\sqrt{48}-\sqrt{300{y}^{2}}\)

Mixed Practice

Try it.

\(2\sqrt{8}+6\sqrt{8}-5\sqrt{8}\)

Solution

\(6\sqrt{2}\)

Try it.

\(\frac{2}{3}\sqrt{27}+\frac{3}{4}\sqrt{48}\)

Try it.

\(\sqrt{175{k}^{4}}-\sqrt{63{k}^{4}}\)

Solution

\(2{k}^{2}\sqrt{7}\)

Try it.

\(\frac{5}{6}\sqrt{162}+\frac{3}{16}\sqrt{128}\)

Try it.

\(2\sqrt{363}-2\sqrt{300}\)

Solution

\(2\sqrt{3}\)

Try it.

\(\sqrt{150}+4\sqrt{6}\)

Try it.

\(9\sqrt{2}-8\sqrt{2}\)

Solution

\(\sqrt{2}\)

Try it.

\(5\sqrt{x}-8\sqrt{y}\)

Try it.

\(8\sqrt{13}-4\sqrt{13}-3\sqrt{13}\)

Solution

\(\sqrt{13}\)

Try it.

\(5\sqrt{12{c}^{4}}-3\sqrt{27{c}^{6}}\)

Try it.

\(\sqrt{80{a}^{5}}-\sqrt{45{a}^{5}}\)

Solution

\({a}^{2}\sqrt{5a}\)

Try it.

\(\frac{3}{5}\sqrt{75}-\frac{1}{4}\sqrt{48}\)

Try it.

\(21\sqrt{19}-2\sqrt{19}\)

Solution

\(19\sqrt{19}\)

Try it.

\(\sqrt{500}+\sqrt{405}\)

Try it.

\(\frac{5}{6}\sqrt{27}+\frac{5}{8}\sqrt{48}\)

Solution

\(5\sqrt{3}\)

Try it.

\(11\sqrt{11}-10\sqrt{11}\)

Try it.

\(\sqrt{75}-\sqrt{108}\)

Solution

\(\text{-}\sqrt{3}\)

Try it.

\(2\sqrt{98}-4\sqrt{72}\)

Try it.

\(4\sqrt{24{x}^{2}}-\sqrt{54{x}^{2}}+3x\sqrt{6}\)

Solution

\(8x\sqrt{6}\)

Try it.

\(8\sqrt{80{y}^{6}}-6\sqrt{48{y}^{6}}\)

Condensed: the full section is in OpenStax Elementary Algebra 2e.

Now you Không máy tính nào có thể tính toán được nó, nhưng các mảnh của nó có thể tính toán được. Thử một trong những cách dưới đây, hoặc gõ theo ý bạn.

Luyện tập (40)

Đầu tiên thử mỗi câu trên giấy. Cho thấy câu trả lời để kiểm tra; những câu trả lời đã kiểm tra có thể mở trong trình giải cho mỗi bước.

  1. Add: ⓐ \(3x+9x\) ⓑ \(5m+5n\).

    Giải đáp

    ⓐ \(12x\) ⓑ \(5m+5n\)

  2. Simplify: \(\sqrt{50{x}^{3}}\).

    Giải đáp

    \(5x\sqrt{2x}\)

  3. Simplify: \(2\sqrt{2}-7\sqrt{2}\).

    Giải đáp

    \(2\sqrt{2}-7\sqrt{2}\)
    Since the radicals are like, we subtract the coefficients.\(-5\sqrt{2}\)

  4. Simplify: \(8\sqrt{2}-9\sqrt{2}\).

    Giải đáp

    \(\text{-}\sqrt{2}\)

  5. Simplify: \(5\sqrt{3}-9\sqrt{3}\).

    Giải đáp

    \(-4\sqrt{3}\)

  6. Simplify: \(3\sqrt{y}+4\sqrt{y}\).

    Giải đáp

    \(3\sqrt{y}+4\sqrt{y}\)
    Since the radicals are like, we add the coefficients.\(7\sqrt{y}\)

  7. Simplify: \(2\sqrt{x}+7\sqrt{x}\).

    Giải đáp

    \(9\sqrt{x}\)

  8. Simplify: \(5\sqrt{u}+3\sqrt{u}\).

    Giải đáp

    \(8\sqrt{u}\)

  9. Simplify: \(4\sqrt{x}-2\sqrt{y}\).

    Giải đáp

    \(4\sqrt{x}-2\sqrt{y}\)
    Since the radicals are not like, we cannot
    subtract them. We leave the expression as is.    		\(4\sqrt{x}-2\sqrt{y}\)

  10. Simplify: \(7\sqrt{p}-6\sqrt{q}\).

    Giải đáp

    \(7\sqrt{p}-6\sqrt{q}\)

  11. Simplify: \(6\sqrt{a}-3\sqrt{b}\).

    Giải đáp

    \(6\sqrt{a}-3\sqrt{b}\)

  12. Simplify: \(5\sqrt{13}+4\sqrt{13}+2\sqrt{13}\).

    Giải đáp

    \(5\sqrt{13}+4\sqrt{13}+2\sqrt{13}\)
    Since the radicals are like, we add the coefficients.\(11\sqrt{13}\)

  13. Simplify: \(4\sqrt{11}+2\sqrt{11}+3\sqrt{11}\).

    Giải đáp

    \(9\sqrt{11}\)

  14. Simplify: \(6\sqrt{10}+2\sqrt{10}+3\sqrt{10}\).

    Giải đáp

    \(11\sqrt{10}\)

  15. Simplify: \(2\sqrt{6}-6\sqrt{6}+3\sqrt{3}\).

    Giải đáp

    \(2\sqrt{6}-6\sqrt{6}+3\sqrt{3}\)
    Since the first two radicals are like, we
    subtract their coefficients.    		\(-4\sqrt{6}+3\sqrt{3}\)

  16. Simplify: \(5\sqrt{5}-4\sqrt{5}+2\sqrt{6}\).

    Giải đáp

    \(\sqrt{5}+2\sqrt{6}\)

  17. Simplify: \(3\sqrt{7}-8\sqrt{7}+2\sqrt{5}\).

    Giải đáp

    \(-5\sqrt{7}+2\sqrt{5}\)

  18. Simplify: \(2\sqrt{5n}-6\sqrt{5n}+4\sqrt{5n}\).

    Giải đáp

    \(2\sqrt{5n}-6\sqrt{5n}+4\sqrt{5n}\)
    Since the radicals are like, we combine them.\(0\sqrt{5n}\)
    Simplify.0

  19. Simplify: \(\sqrt{7x}-7\sqrt{7x}+4\sqrt{7x}\).

    Giải đáp

    \(-2\sqrt{7x}\)

  20. Simplify: \(4\sqrt{3y}-7\sqrt{3y}+2\sqrt{3y}\).

    Giải đáp

    \(\text{-}\sqrt{3y}\)

  21. Simplify: \(\sqrt{3xy}+5\sqrt{3xy}-4\sqrt{3xy}\).

    Giải đáp

    \(\sqrt{3xy}+5\sqrt{3xy}-4\sqrt{3xy}\)
    Since the radicals are like, we combine them.\(2\sqrt{3xy}\)

  22. Simplify: \(\sqrt{5xy}+4\sqrt{5xy}-7\sqrt{5xy}\).

    Giải đáp

    \(-2\sqrt{5xy}\)

  23. Simplify: \(3\sqrt{7mn}+\sqrt{7mn}-4\sqrt{7mn}\).

    Giải đáp

    \(0\)

  24. Simplify: \(\sqrt{20}+3\sqrt{5}\).

    Giải đáp

    \(\sqrt{20}+3\sqrt{5}\)
    Simplify the radicals, when possible.\(\sqrt{4}\cdot \sqrt{5}+3\sqrt{5}\)
    \(2\sqrt{5}+3\sqrt{5}\)
    Combine the like radicals.\(5\sqrt{5}\)

  25. Simplify: \(\sqrt{18}+6\sqrt{2}\).

    Giải đáp

    \(9\sqrt{2}\)

  26. Simplify: \(\sqrt{27}+4\sqrt{3}\).

    Giải đáp

    \(7\sqrt{3}\)

  27. Simplify: \(\sqrt{48}-\sqrt{75}\).

    Giải đáp

    \(\sqrt{48}-\sqrt{75}\)
    Simplify the radicals.\(\sqrt{16}\cdot \sqrt{3}-\sqrt{25}\cdot \sqrt{3}\)
    \(4\sqrt{3}-5\sqrt{3}\)
    Combine the like radicals.\(\text{-}\sqrt{3}\)

  28. Simplify: \(\sqrt{32}-\sqrt{18}\).

    Giải đáp

    \(\sqrt{2}\)

  29. Simplify: \(\sqrt{20}-\sqrt{45}\).

    Giải đáp

    \(\text{-}\sqrt{5}\)

  30. Simplify: \(5\sqrt{18}-2\sqrt{8}\).

    Giải đáp

    \(5\sqrt{18}-2\sqrt{8}\)
    Simplify the radicals.\(5\cdot \sqrt{9}\cdot \sqrt{2}-2\cdot \sqrt{4}\cdot \sqrt{2}\)
    \(5\cdot 3\cdot \sqrt{2}-2\cdot 2\cdot \sqrt{2}\)
    \(15\sqrt{2}-4\sqrt{2}\)
    Combine the like radicals.\(11\sqrt{2}\)

  31. Simplify: \(4\sqrt{27}-3\sqrt{12}\).

    Giải đáp

    \(6\sqrt{3}\)

  32. Simplify: \(3\sqrt{20}-7\sqrt{45}\).

    Giải đáp

    \(-15\sqrt{5}\)

  33. Simplify: \(\frac{3}{4}\sqrt{192}-\frac{5}{6}\sqrt{108}\).

    Giải đáp

    \(\frac{3}{4}\sqrt{192}-\frac{5}{6}\sqrt{108}\)
    Simplify the radicals.\(\frac{3}{4}\sqrt{64}\cdot \sqrt{3}-\frac{5}{6}\sqrt{36}\cdot \sqrt{3}\)
    \(\frac{3}{4}\cdot 8\cdot \sqrt{3}-\frac{5}{6}\cdot 6\cdot \sqrt{3}\)
    \(6\sqrt{3}-5\sqrt{3}\)
    Combine the like radicals.\(\sqrt{3}\)

  34. Simplify: \(\frac{2}{3}\sqrt{108}-\frac{5}{7}\sqrt{147}\).

    Giải đáp

    \(\text{-}\sqrt{3}\)

  35. Simplify: \(\frac{3}{5}\sqrt{200}-\frac{3}{4}\sqrt{128}\).

    Giải đáp

    \(0\)

  36. Simplify: \(\frac{2}{3}\sqrt{48}-\frac{3}{4}\sqrt{12}\).

    Giải đáp

    \(\frac{2}{3}\sqrt{48}-\frac{3}{4}\sqrt{12}\)
    Simplify the radicals.\(\frac{2}{3}\sqrt{16}\cdot \sqrt{3}-\frac{3}{4}\sqrt{4}\cdot \sqrt{3}\)
    \(\frac{2}{3}\cdot 4\cdot \sqrt{3}-\frac{3}{4}\cdot 2\cdot \sqrt{3}\)
    \(\frac{8}{3}\sqrt{3}-\frac{3}{2}\sqrt{3}\)
    Find a common denominator to subtract the
    coefficients of the like radicals.    		\(\frac{16}{6}\sqrt{3}-\frac{9}{6}\sqrt{3}\)
    Simplify.\(\frac{7}{6}\sqrt{3}\)

  37. Simplify: \(\frac{2}{5}\sqrt{32}-\frac{1}{3}\sqrt{8}\).

    Giải đáp

    \(\frac{14}{15}\sqrt{2}\)

  38. Simplify: \(\frac{1}{3}\sqrt{80}-\frac{1}{4}\sqrt{125}\).

    Giải đáp

    \(\frac{1}{12}\sqrt{5}\)

  39. Simplify: \(\sqrt{18{n}^{5}}-\sqrt{32{n}^{5}}\).

    Giải đáp

    \(\sqrt{18{n}^{5}}-\sqrt{32{n}^{5}}\)
    Simplify the radicals.\(\sqrt{9{n}^{4}}\cdot \sqrt{2n}-\sqrt{16{n}^{4}}\cdot \sqrt{2n}\)
    \(3{n}^{2}\sqrt{2n}-4{n}^{2}\sqrt{2n}\)
    Combine the like radicals.\(\text{-}{n}^{2}\sqrt{2n}\)

  40. Simplify: \(\sqrt{32{m}^{7}}-\sqrt{50{m}^{7}}\).

    Giải đáp

    \(\text{-}{m}^{3}\sqrt{2m}\)

Để cho anh làm việc

Một tài khoản miễn phí thêm ghi chú vào mỗi bài học, ghi chép những gì bạn đã hoàn thành, các bài toán bạn giải quyết ở một nơi, và một giáo viên bạn có thể hỏi về trang này. Toán học là mở cho mọi người, dù có đăng nhập hay không.

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Làm thế nào: Add and Subtract Square Roots

  1. Add and subtract like square roots
  2. Add and subtract square roots that need simplification
  3. To add or subtract like square roots, add or subtract the coefficients and keep the like square root.
  4. Sometimes when we have to add or subtract square roots that do not appear to have like radicals, we find like radicals after simplifying the square roots.

Câu hỏi người ta hỏi

What does it mean to solve an equation?

To find every value of the unknown that makes both sides equal. Each step is an operation applied to both sides that keeps the solution set the same, until the unknown stands alone.

Why do I sometimes get two answers?

A quadratic can cross the axis twice, so it can have two solutions. A degree-n polynomial has up to n. The graph shows where each one comes from.

How do I know whether to factor or use the quadratic formula?

Try factoring for a few seconds: look for two numbers that multiply to a·c and add to b. If nothing obvious appears, the discriminant b² − 4ac tells you how many real roots there are, and the formula finds them without guessing.

Một số phần của trang này được chuyển từ OpenStax Elementary Algebra 2e (CC BY-NC-SA 4.0). Được nén lại và giải thích lại ở đây; lỗi là của chúng tôi. Bởi vì nguồn của nó được cấp phép cho sử dụng không thương mại, bài học này là miễn phí, không bán gì, và được chia sẻ dưới cùng một giấy phép.

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