grelaratzuvy

2023-03-11

What is the square root of 32 over 4, expressed in the simplest radical form?

### Answer & Explanation

kizintefevd3

Determine the square root of 32 over 4, expressed in the simplest radical form.
When a number is multiplied by itself, its square root returns the original number.
Find the prime factors of $\frac{32}{4}$:
$\frac{32}{4}=\frac{2×4×4}{2×2}$
Take square root from both sides of the above equation:
$\sqrt{\frac{32}{4}}=\sqrt{\frac{2×4×4}{2×2}}\phantom{\rule{0ex}{0ex}}⇒\sqrt{\frac{32}{4}}=\frac{\sqrt{2×4×4}}{\sqrt{2×2}}\phantom{\rule{0ex}{0ex}}⇒\sqrt{\frac{32}{4}}=\frac{4}{2}\sqrt{2}\phantom{\rule{0ex}{0ex}}⇒\sqrt{\frac{32}{4}}=2\sqrt{2}$
Thus, the square root of 32 over 4, expressed in the simplest radical form is $2\sqrt{2}$

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