What is the square root of 4/125?

Question

2230 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-09T22:25:00

$\sqrt{\frac{4}{125}} = \frac{2 \sqrt{5}}{25}$ $sqrt(4/125)=(2sqrt 5)/(25)$

$\sqrt{\frac{4}{125}}$ $sqrt(4/125)$

Simplify.

$\frac{\sqrt{4}}{\sqrt{125}}$ $(sqrt 4)/(sqrt125)$

Determine the prime factors for $4$ $4$ and $125$ $125$ .

$\frac{\sqrt{2 \times 2}}{\sqrt{5 \times 5 \times 5}}$ $(sqrt(2xx2))/(sqrt(5xx5xx5))$

$\frac{\sqrt{2^{2}}}{\sqrt{5^{2} \times 5}}$ $(sqrt(2^2))/(sqrt(5^2xx5)$

Apply square root rule $\sqrt{a^{2}} = a$ $sqrt(a^2)=a$ .

$\frac{2}{5 \sqrt{5}}$ $2/(5sqrt 5)$

Rationalize the denominator.

$\frac{2}{5 \sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} =$ $2/(5sqrt 5)xx(sqrt5)/(sqrt5)=$

$\frac{2 \sqrt{5}}{5 \sqrt{5} \sqrt{5}} =$ $(2sqrt 5)/(5sqrt5sqrt5)=$

Simplify $\sqrt{5} \sqrt{5}$ $sqrt 5sqrt 5$ to $5$ $5$ .

$\frac{2 \sqrt{5}}{5 \times 5} =$ $(2sqrt 5)/(5xx5)=$

$\frac{2 \sqrt{5}}{25}$ $(2sqrt 5)/(25)$