How do you simplify sqrt(10/21)?

1 Answer
May 16, 2017

Answer: sqrt(210)/21

Explanation:

Simplify: sqrt(10/21)

First we can write out the prime factorization of each value inside the square root:
=sqrt((2*5)/(3*7))
Since there are no common factors in the numerator and denominator, we determine that 10 an 21 are in fact relatively prime. So, we now simply rationalize the denominator by multiplying the numerator and denominator by sqrt(21)
=sqrt(10/21)*sqrt(21/21)
=sqrt(210)/21 which is our final answer