Roots as Inverse Growth Math Example 3

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

Example 3

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

Solution

  1. 1
    \(\sqrt{144}\): what number squared is 144? \(12^2 = 144\), so \(\sqrt{144} = 12\).
  2. 2
    \(\sqrt[3]{27}\): what number cubed is 27? \(3^3 = 27\), so \(\sqrt[3]{27} = 3\).

Answer

\(\sqrt{144} = 12\); \(\sqrt[3]{27} = 3\)
Square root undoes squaring; cube root undoes cubing. Both are inverse operations of their respective 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 1 easy

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

Example 2 medium

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

Example 4 medium

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

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