Question

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

Answer 1

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