Rationalise the denominator of the following: | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) To rationalise the denominator,multiply the numerator and the denominator by the conjugate of the denominator,which is $(\sqrt{5}+\sqrt{3})$.$\fra

Vedclass · Accepted Answer

$9+2 \sqrt{15}$

Vedclass · Answer

(C) To rationalise the denominator,multiply the numerator and the denominator by the conjugate of the denominator,which is $(\sqrt{5}+\sqrt{3})$.$\frac{3 \sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} 	imes \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}$$= \frac{3(\sqrt{5})^2 + 3\sqrt{15} + \sqrt{15} + (\sqrt{3})^2}{(\sqrt{5})^2 - (\sqrt{3})^2}$$= \frac{3(5) + 4\sqrt{15} + 3}{5 - 3}$$= \frac{15 + 4\sqrt{15} + 3}{2}$$= \frac{18 + 4\sqrt{15}}{2}$$= \frac{2(9 + 2\sqrt{15})}{2}$$= 9 + 2\sqrt{15}$

Rationalise the denominator of the following:
$\frac{3 \sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

Similar Questions

The product $\sqrt[3]{2} \cdot \sqrt[4]{2} \cdot \sqrt[12]{32}$ equals

If $a = 2 + \sqrt{3}$,then find the value of $a - \frac{1}{a}$.

Classify the following numbers as rational or irrational with justification:
$(i)$ $\sqrt{196}$
$(ii)$ $3\sqrt{18}$

After rationalizing the denominator of $\frac{7}{3 \sqrt{3}-2 \sqrt{2}},$ we get the denominator as

If $x = 5 + 2\sqrt{6}$,then find the value of $x^{2} + \frac{1}{x^{2}}$ and $x^{3} + \frac{1}{x^{3}}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Rationalise the denominator of the following:$\frac{3 \sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$