How do you find the value of 3 square root of 125?

1 Answer
Sep 9, 2015

Answer:

#3 xx sqrt125 = 15sqrt5# and #root(3)125 = 5#

Explanation:

I have heard many students read #root(3)n# as "the third square root of n". This is a mistake. The square root is #root(2)n# (usually denoted #sqrtx#), the third (or cube) root is #root(3)n#, the fourth root is #root(4)n# and so on.

Whichever was meant the first step for simplifying is the same. Factor the radicand (the thing under the root symbol)

#125 = 5xx25 = 5xx5xx5 = 5^3#

so

#3sqrt125 =3 xx sqrt (25xx5) = 3xx sqrt25 xx sqrt5 = 3xx5xx sqrt5 = 15sqrt5#

And

#root(3)125 = root(3) (5^3) = 5#