How do you simplify #sqrt(10/21)#?

1 Answer
Y
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

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