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

# Question Video: Estimation of Square and Cube Roots to Compare Two Numbers Mathematics • Second Year of Preparatory School

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Without calculating, determine if √(121) is greater than, equal to, or less than ∛(−42).

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### Video Transcript

Without calculating, determine if the square root of 121 is greater than, equal to, or less than the cube root of negative 42.

The key to this question is we’re asked to answer it without calculating the square root of 121 or the cube root of negative 42. As a result, we need to recall some key properties of square rooting and cube rooting numbers. Let’s begin by recalling what happens when we square root positive and negative numbers. Square rooting any positive number gives us a positive answer. When we attempt to square root a negative number, there are no real solutions. In this question, we have the square root of 121. And since 121 is positive, the square root of 121 will also be positive and is therefore greater than zero.

Let’s now consider what happens when we cube root positive and negative numbers. The cube root of any positive number gives us a positive answer, whereas the cube root of any negative number gives a negative answer. In this question, we have the cube root of negative 42. This will give us a negative answer, which is therefore less than zero.

We can therefore conclude that the square root of 121 is greater than the cube root of negative 42, since any positive number will be greater than any negative number. The correct answer is greater than.

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