Rationalise the following:
$\frac{3+√5}{3-√5}$

Given:  $\frac{3+√5}{3-√5}$

To do: Rationalize the given number

Solution:

$\frac{3+√5}{3-√5}$

[Multiply and divide by $3+\sqrt{5}$]

=$\frac{3+√5}{3-√5}  \times  \frac{3+√5}{3+√5}$ 

Numerator- $(a+b)(a+b)=(a+b)^2$

Denominator- $(a-b)(a+b)=a^2-b^2$

=$\frac{(3+√5)^{2}}{3^{2}-√5^{2}}$

= $\frac{3^{2} + 2 \times 3 \times  √5 + (√5)^2} {9 - 5}$

= $\frac{9 +6√5 + 5}{4}$

= $\frac{14 + 6√5}{4} $

= $\frac{7+3√5}{2}$ Ans

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

23 Views

Kickstart Your Career

Get certified by completing the course

Get Started