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Powers and roots
Exponent rules and simplifying square roots exactly.
A square root is simplified by pulling out the largest perfect square: √50 = √(25·2) = 5√2. Exponent rules (aᵐ·aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁻ⁿ = 1/aⁿ) let you rewrite powers without computing them.
Вработен пример: sqrt(50)
Чекор по чекор
- \sqrt{50} = 5 \sqrt{2}
Evaluate.
Одкриј го одговорот
Symbols used here
The non-negative number whose square (n-th power) is x.
Equal to the precision shown, not exactly.
Both signs at once: x = 3 ± 2 means 5 and 1.
The two sides are different.
Inequalities that allow equality; < and > exclude it.
What is left after dividing a by n.
Per hundred: 15% = 15/100.
a for every b; a divided by b.
How to: Powers and roots
- Evaluate.
Questions people ask
Why does the order of operations matter?
Because 2 + 3 × 4 would otherwise be two different numbers. The convention (brackets, exponents, multiplication and division, addition and subtraction) exists so every reader gets the same value from the same expression.
How do I check an arithmetic answer?
Estimate first (round every number and compute roughly), then compare. If the estimate and the exact answer disagree by more than a little, one of them is wrong. The solver shows every operation, so you can find which line went astray.
Why are fractions harder than decimals?
They are not harder, they are more exact: 1/3 is a precise number, 0.333 is an approximation. Fractions need a common denominator to add, which is the one extra step people trip on.