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.
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.
$ 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.
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 $\sqrt{15\over9} = \frac{\sqrt{15}}{\sqrt9} = \frac{\sqrt{15}}3$
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 :)