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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.

Àwọn ààtò àwọn ìṣàmúlò-ètò · sqrt(50)

Arithmetic · Arithmetic

Evaluate sqrt(50)

\sqrt{50}

Àwọn ìṣàmúlò-ètò

\sqrt{50} = 5 \sqrt{2}
Evaluate.

Fi àwọn àgbèwọlé hàn

5 \sqrt{2} \approx 7.0711

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Bii o ṣe le: Powers and roots

Evaluate.

Àwọn Àtòjọ-ẹ̀yàn

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.

Diẹ̀ nínú Arithmetic

Order of operations Fractions Percentages