What is the square root of 4/125?

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Answer 1 · 2015-10-09T22:25:00

$sqrt(4/125)=(2sqrt 5)/(25)$

$sqrt(4/125)$

Simplify.

$(sqrt 4)/(sqrt125)$

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

$(sqrt(2xx2))/(sqrt(5xx5xx5))$

$(sqrt(2^2))/(sqrt(5^2xx5)$

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

$2/(5sqrt 5)$

Rationalize the denominator.

$2/(5sqrt 5)xx(sqrt5)/(sqrt5)=$

$(2sqrt 5)/(5sqrt5sqrt5)=$

Simplify $sqrt 5sqrt 5$ to $5$ .

$(2sqrt 5)/(5xx5)=$

$(2sqrt 5)/(25)$