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Chapter 5: Problem 101

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(\frac{\sqrt{64}}{2}=\sqrt{32}\)

Short Answer

Expert verified
The statement \(\frac{\sqrt{64}}{2}=\sqrt{32}\) is false. To make it true, we should write \(\frac{\sqrt{64}}{2}=4\).

Step by step solution

01

Simplify the numerator

The expression is \(\frac{\sqrt{64}}{2}\). We know that the square root of 64 is 8. So, rewrite the expression as \(\frac{8}{2}\).
02

Perform the division

Perform the division in the fraction. 8 divided by 2 equals 4.
03

Compare the results

On the right side of the equation, we have \(\sqrt{32}\), which is approximately 5.66. On the left side, we found 4. So, 4 does not equal \(\sqrt{32}\), hence the statement is false.
04

Fix the false statement

To make the statement true, we would need to adjust the right side to say 4 instead of \(\sqrt{32}\), making the statement \(\frac{\sqrt{64}}{2}=4\), which is a true statement.

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