How do you simplify √250252?

1 Answer
Adam L.
Mar 14, 2017

5⋅√53⋅√14

Explanation:

First, simplify the fraction in the square root:
√125126
Then, use the rule√ab=√a√b:
√125√126
Now, onto simplifying the radicals on the top and bottom: split the square roots using the rule √ab=√a⋅√b:
√25⋅√5√9⋅√14 (see notes below if this doesn't make sense)
Simplify √25 and √9:
5⋅√53⋅√14
And that's as far as you can go!

Note on simplification of √125 & √126:
The way I used to simplify these is to find all the prime factors:
√125=√5⋅√5⋅√5
√126=√2⋅√3⋅√3⋅√7
Since √5⋅√5=√52=5 and √3⋅√3=√32=3, you can simplify these to:
√125=5⋅√5
√126=√2⋅3⋅√7
Using the rule √ab=√a⋅√b on the second expression:
√125=5⋅√5
√126=3⋅√14
And you end up in the same place as the first method

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
3079 views around the world
You can reuse this answer
Creative Commons License