Practice Roots as Inverse Growth in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Understanding roots as undoing exponentiation—finding what was raised to a power.

If 3^2 = 9, then \sqrt{9} = 3. The root asks: 'What number squared gives 9?'

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 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.