simplify \(\frac{10}{\sqrt{32}}\)
Question 1 Report
simplify \(\frac{10}{\sqrt{32}}\)
Answer Details
We can simplify \(\frac{10}{\sqrt{32}}\) by rationalizing the denominator, which means we multiply both the numerator and denominator by the same number so that the denominator becomes a rational number (i.e., a number that can be written as a fraction).
In this case, we can multiply the numerator and denominator by \(\sqrt{32}\), since \(\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}\).
So we have:
$$\frac{10}{\sqrt{32}} \times \frac{\sqrt{32}}{\sqrt{32}} = \frac{10\sqrt{32}}{32} = \frac{5\sqrt{2}}{4}$$
Therefore, the answer is \(\frac{5}{4}\sqrt{2}\).
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