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
Roots reverse the process of exponentiation: the nth root of a finds the number that, raised to the nth power, produces a. For example, \sqrt[3]{8} = 2 because 2^3 = 8.
If 3^2 = 9, then \sqrt{9} = 3. The root asks: 'What number squared gives 9?'
Example 1
easySince \(8^2 = 64\), what is \(\sqrt{64}\)? Explain roots as inverses of powers.
Example 2
mediumEstimate \(\sqrt{50}\) to one decimal place by finding the two perfect squares it lies between.
Example 3
easyFind \(\sqrt{144}\) and \(\sqrt[3]{27}\).
Example 4
mediumBetween which two consecutive integers does \(\sqrt{75}\) lie? Estimate to one decimal.