Question

rationalise the denominator 4root 3 +5root 2 /4 root 3 +3root2

Answer 1

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:

[Remember: $\sqrt{48}$ = 4$\sqrt{3}$ & $\sqrt{18}$ =3 $\sqrt{2}$ ]

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

$\bold{(a+b)(a-b)=a^{2}-b^{2}}$

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

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

By rationalizing the denominator of $\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$ we get as$\bold{\frac{9+4 \sqrt{6}}{15}}$ the answer.

Hope this will help you ! :)