Video: Estimation of Square and Cube Roots to Compare Two Numbers

Is √121 greater than, equal to, or less than ∛−42?

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Video Transcript

Is the square root of 121 greater than, equal to, or less than the cube root of negative 42?

We know that the positive square root of 121 is equal to 11 since 11 multiplied by 11 is equal to 121. One way to answer this question would be to type the cube root of negative 42 into the calculator. However, what would happen if we didn’t have a calculator.

Well, the cube root of any negative number is always negative. Likewise, the cube root of a positive number is always positive. This means that the cube root of negative 42 will give a negative answer. Therefore, the square root of 121, which is 11, is greater than the cube root of negative 42.

Typing the cube root of negative 42 into the calculator to check gives us an answer of negative 3.48 to two decimal places. As 11 is greater than negative 3.48, our answer is correct.

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