Question

rationalize the denominator of 4 root 3 + 5 root 2/root 48 + root 18

Answer 1

Check it out...hope it helps

Answer 2

Answer:

By rationalizing the denominator of $\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$ we get

$\bold{\frac{9+4 \sqrt{6}}{15}}$

Step-by-step explanation:

Rationalizing the denominator means multiplying the numerator in a fraction by the value of the denominator but by its opposite signed value.

Now to rationalize the above figure we multiply both the numerator and denominator by [√48-√18]

$\left[\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}\right]\left[\frac{\sqrt{48}-\sqrt{18}}{\sqrt{48}-\sqrt{18}}\right]$

On removing the brackets and multiplying,

The denominator is multiplied by using the formula $\bold{(a+b)(a-b)=a^{2}-b^{2}}$

$\begin{aligned} &=\left[\frac{4 \sqrt{3}(\sqrt{48}-\sqrt{18})+5 \sqrt{2}(\sqrt{48}-\sqrt{18})}{48-18}\right] \\ &=\left[\frac{4 \sqrt{3}(\sqrt{48}-\sqrt{18})+5 \sqrt{2}(\sqrt{48}-\sqrt{18})}{30}\right] \\ &=\left[\frac{4 \sqrt{3} \sqrt{48}-4 \sqrt{3} \sqrt{18}+5 \sqrt{2} \sqrt{48}-5 \sqrt{2} \sqrt{18}}{30}\right] \\ &=\left[\frac{18+8 \sqrt{6}}{30}\right] \end{aligned}$

By rationalizing the denominator of $\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$ we get

$\bold{\frac{9+4 \sqrt{6}}{15}}$ as the answer.