Roots as Inverse Growth Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Since \(8^2 = 64\), what is \(\sqrt{64}\)? Explain roots as inverses of powers.

Solution

  1. 1
    We know \(8^2 = 64\) (squaring).
  2. 2
    The square root undoes squaring: \(\sqrt{64} = 8\).
  3. 3
    Check: \(8 \times 8 = 64\) ✓
  4. 4
    Root is the inverse operation of the corresponding power.

Answer

\(\sqrt{64} = 8\)
A square root answers: what number times itself gives this result? Since \(8^2=64\), \(\sqrt{64}=8\). Roots undo powers.

About Roots as Inverse Growth

Roots reverse the process of exponentiation: the nnth root of aa finds the number that, raised to the nnth power, produces aa. For example, 83=2\sqrt[3]{8} = 2 because 23=82^3 = 8.

Learn more about Roots as Inverse Growth →

More Roots as Inverse Growth Examples

Example 2 medium

Estimate (sqrt{50}) to one decimal place by finding the two perfect squares it lies between.

Example 3 easy

Find (sqrt{144}) and (sqrt[3]{27}).

Example 4 medium

Between which two consecutive integers does (sqrt{75}) lie? Estimate to one decimal.

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