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 th root of finds the number that, raised to the th power, produces . For example, because .
If , then . The root asks: 'What number squared gives 9?'
Showing a random 20 of 50 problems.
Example 1
easyFind .
Example 2
easyFind and .
Example 3
challengeFor which real numbers does hold, and where does it fail? Justify.
Example 4
mediumEstimate to one decimal place by bracketing it between perfect squares.
Example 5
easyTrue or false: .
Example 6
mediumSolve for , and verify your answer.
Example 7
mediumA square has area and you find its side is . What was , and what operation recovers the side from ?
Example 8
easyIs equal to ?
Example 9
easyFind .
Example 10
easyFind .
Example 11
mediumSimplify .
Example 12
mediumBetween which two consecutive integers does lie? Estimate to one decimal.
Example 13
hardSimplify .
Example 14
hardRationalize and simplify .
Example 15
easyFind .
Example 16
mediumSolve for real .
Example 17
mediumA square's area grows from to . By what factor does its side grow?
Example 18
mediumSolve for all real .
Example 19
easySince , what is ? Explain roots as inverses of powers.
Example 20
mediumWhich is larger: or ?