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

May 16, 2017

Answer: $\frac{\sqrt{210}}{21}$

#### Explanation:

Simplify: $\sqrt{\frac{10}{21}}$

First we can write out the prime factorization of each value inside the square root:
$= \sqrt{\frac{2 \cdot 5}{3 \cdot 7}}$
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 $\sqrt{21}$
$= \sqrt{\frac{10}{21}} \cdot \sqrt{\frac{21}{21}}$
$= \frac{\sqrt{210}}{21}$ which is our final answer