grelaratzuvy

2023-03-11

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

kizintefevd3

Beginner2023-03-12Added 4 answers

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 $\frac{32}{4}$:

$\frac{32}{4}=\frac{2\times 4\times 4}{2\times 2}$

Take square root from both sides of the above equation:

$\sqrt{\frac{32}{4}}=\sqrt{\frac{2\times 4\times 4}{2\times 2}}\phantom{\rule{0ex}{0ex}}\Rightarrow \sqrt{\frac{32}{4}}=\frac{\sqrt{2\times 4\times 4}}{\sqrt{2\times 2}}\phantom{\rule{0ex}{0ex}}\Rightarrow \sqrt{\frac{32}{4}}=\frac{4}{2}\sqrt{2}\phantom{\rule{0ex}{0ex}}\Rightarrow \sqrt{\frac{32}{4}}=2\sqrt{2}$

Thus, the square root of 32 over 4, expressed in the simplest radical form is $2\sqrt{2}$

When a number is multiplied by itself, its square root returns the original number.

Find the prime factors of $\frac{32}{4}$:

$\frac{32}{4}=\frac{2\times 4\times 4}{2\times 2}$

Take square root from both sides of the above equation:

$\sqrt{\frac{32}{4}}=\sqrt{\frac{2\times 4\times 4}{2\times 2}}\phantom{\rule{0ex}{0ex}}\Rightarrow \sqrt{\frac{32}{4}}=\frac{\sqrt{2\times 4\times 4}}{\sqrt{2\times 2}}\phantom{\rule{0ex}{0ex}}\Rightarrow \sqrt{\frac{32}{4}}=\frac{4}{2}\sqrt{2}\phantom{\rule{0ex}{0ex}}\Rightarrow \sqrt{\frac{32}{4}}=2\sqrt{2}$

Thus, the square root of 32 over 4, expressed in the simplest radical form is $2\sqrt{2}$