Question

Rationalise 4 root 3 +5root2/4 root 3+3 root 2

Answer 1

Answer:

The rationalization of $\frac{4\sqrt{3}+5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}$ is $\frac{9+4\sqrt{6}}{15}$

Step-by-step explanation:

Given : 4 root 3 +5 root 2/4 root 3+3 root 2

To find : Rationalize the given expression?

Solution :

The given expression is $\frac{4\sqrt{3}+5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}$

Rationalizing the expression by multiplying and dividing denominator with opposite sign,

$=\frac{4\sqrt{3}+5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}\times \frac{4\sqrt{3}-3\sqrt{2}}{4\sqrt{3}-3\sqrt{2}}$

The denominator is multiplied by using the formula,

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

$=\frac{(4\sqrt{3})^2-(4\sqrt{3})(3\sqrt2)+(5\sqrt{2})(4\sqrt{3})-(5\sqrt{2})(3\sqrt{2})}{(4\sqrt{3})^2-(3\sqrt{2})^2}$

$=\frac{48-12\sqrt{6}+20\sqrt{6}-30}{48-18}$

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

Therefore, The rationalization of $\frac{4\sqrt{3}+5\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}$ is $\frac{9+4\sqrt{6}}{15}$

Answer 2

Answer:

i hope it's helpful for you