How to convert $\sqrt{\frac{5}{3}}$ to $\frac{\sqrt{15}}{3}$? Disclosure: This is homework, but not part of the homework. This is just something that I do not understand.

$$ x = \sqrt{\frac{5}{3}} $$
$$ x = \frac{\sqrt{15}}{3} $$

Could anyone please explain this to me?
Thanks in advance.
 A: 
$$ x= \sqrt{\frac{5}{3}} = \frac{\sqrt{5}}{\sqrt{3}} =\frac{\sqrt{5} \times\sqrt{3} }{\sqrt{3}\times \sqrt{3}} = \frac{\sqrt{15}}{3}$$

This is called rationalizing the denominator, you can practice more here.
A: If you have the root $\sqrt{5/3}$, you can simply extend by three, yielding $\sqrt{15/9}$. Then you can proceed by the laws for roots and get
$$\sqrt{15\over9} = \frac{\sqrt{15}}{\sqrt9} = \frac{\sqrt{15}}3$$
A: Multiply top and bottom of the fraction by $\sqrt{3}$ and you get $\sqrt{3} \cdot \sqrt{5}=\sqrt{15}$ on top and $\sqrt{3} \cdot \sqrt{3}=3$ on the bottom. The trick is to multiply the fraction by the bottom square root, thus getting rid of the square root in the bottom of the fraction. Mathematicians don't like square roots on the bottom of fraction :) 
A: Well lets think about it. All we can do to change this so that it is exactly equal is to multiply the top and bottom by the same value. We can also easily say that $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$
Putting this into terms of this question... $\frac{\sqrt{5}}{\sqrt{3}} = \sqrt{\frac{5}{3}}$
We can also that that $\sqrt{n} \times \sqrt{n} = n$. In other words, the square root of any positive number $n$ times itself is equal to $n$. Since the bottom number is equal to 3 in the converted from, we can simply multiply the numerator and denominator by $\sqrt{3}$
$\frac{\sqrt{5}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{15}}{\sqrt{9}} = \frac{\sqrt{15}}{3}$
I hope that clears things up!
A: $$\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$$
Since $\frac{\sqrt{b}}{\sqrt{b}}=1$, then we can multiply the right hand side of the above expression by $\frac{\sqrt{b}}{\sqrt{b}}$, we get:
$$\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}} \times \frac{\sqrt{b}}{\sqrt{b}}$$
Note that $\sqrt{a} \times \sqrt{b}=\sqrt{ab}$ , and note that $\sqrt{b} \times \sqrt{b}=\sqrt{b}^2=b$.
Therefore,
$$\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}} \times \frac{\sqrt{b}}{\sqrt{b}}=\frac{\sqrt{ab}}{b}$$
In this case,
$$\sqrt{\frac{5}{3}}=\frac{\sqrt{5}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{5 \cdot 3}}{3}=\frac{\sqrt{15}}{3}$$
This question was asked long time before, but I answer it in his way because I think someone will see his answer and will get use of it.
