Question

rationalize this right now​

Answer 1

ANSWER IN ATTACHEMENT

Regards

Akshat Rajput

◼ MATHS ARYABHATTA

◼ BRAINLY CHALLENGER

Answer 2

Answer:

Step-by-step explanation:

Given :

To rationalise the denominator of the fraction

$\frac{\sqrt{5}+5}{\sqrt{6}+\sqrt{5}}$

Solution :

We know that,

The denominator of the fraction are under square roots,

So,

We shall use the algorithm of the identity :

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

Let a = $\sqrt{6}$ & b = $\sqrt{5}$

So,.

It will become $(\sqrt{6}+\sqrt{5})(\sqrt{6}-\sqrt{5}) = (\sqrt{6})^2-(\sqrt{5})^2 = 6 - 5 = 1$

So,

By multiplying (\sqrt{6}-\sqrt{5}) on both numerator & denominator,

We get,

⇒ $\frac{\sqrt{5}+5}{\sqrt{6}+\sqrt{5}} \times \frac{\sqrt{6}-\sqrt{5}}{\sqrt{6}-\sqrt{5}}$

⇒ $\frac{(\sqrt{5}+5)(\sqrt{6}-\sqrt{5})}{(\sqrt{6}+\sqrt{5})(\sqrt{6}-\sqrt{5})}$

⇒  $\frac{(\sqrt{5}+5)(\sqrt{6}-\sqrt{5})}{1}$ (rationalised the denominator),.

⇒  $\sqrt{30} - 5+5\sqrt{6}-5\sqrt{5}$