Question

,rationalize the denominator

1+√2/√5+√3​

Answer 1

Explanation:

(1+√2)(√5-√3)/√5+√3)(√5-√3)

=√5-√3+√10-√6/2

Answer 2

ANSWER:

To Rationalize:

• (1 + √2)/(√5 + √3)

Solution:

$\text{We are given that,}\\\\:\longrightarrow\dfrac{1+\sqrt2}{\sqrt5+\sqrt3}\\\\\text{Multiplying and Dividing by \sqrt5-\sqrt3 ,}\\\\:\implies\dfrac{1+\sqrt2}{\sqrt5+\sqrt3}\times\dfrac{\sqrt5-\sqrt3}{\sqrt5-\sqrt3}\\\\:\implies\dfrac{(1+\sqrt2)(\sqrt5-\sqrt3)}{(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)}\\\\\text{We know that,}$

$:\hookrightarrow(a-b)(a+b)=a^2-b^2\\\\\text{So,}\\\\:\implies\dfrac{(1+\sqrt2)(\sqrt5-\sqrt3)}{(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)}\\\\:\implies\dfrac{\sqrt5-\sqrt3+\sqrt{10}-\sqrt6}{(\sqrt5)^2-(\sqrt3)^2}\\\\:\implies\dfrac{\sqrt5+\sqrt{10}-\sqrt3-\sqrt6}{5-3}$

$\bf{:\implies\dfrac{\sqrt5+\sqrt{10}-\sqrt3-\sqrt6}{2}}\\\\\text{OR,}\\\\:\implies\dfrac{\sqrt5(1+\sqrt2)-\sqrt3(1+\sqrt2)}{2}\\\\\bf{:\implies\dfrac{(1+\sqrt2)(\sqrt5-\sqrt3)}{2}}$

Formula Used:

$:\hookrightarrow(a-b)(a+b)=a^2-b^2$