Question

The simple form of √5-√4/√5+√4

Answer 1

Hello!

$\dfrac{\sqrt{5} - \sqrt{4}}{\sqrt{5} + \sqrt{4}}$

⇒ $\dfrac{\sqrt{5} - 2}{\sqrt{5} + 2} \sf \:x\: \dfrac{\sqrt{5} - 2}{\sqrt{5} - 2}$

⇒ $\dfrac{(\sqrt{5} - 2)^{2}}{(\sqrt{5})^{2} - (2)^{2}}$

⇒ $\dfrac{5 - 4\sqrt{5} + 4}{5 - 4}$

⇒ $\boxed{\sf 9 - 4\sqrt{5}}$

Cheers!

Answer 2

Hello ,

The answer is 9 - 4√5

Here is the explanation
MARK IT AS THE BRAINLIEST,if it helps

$\frac{ \sqrt{5} - \sqrt{4} }{ \sqrt{5} + \sqrt{4} } \times \frac{1}{1} \\ = \frac{ \sqrt{5} - \sqrt{4} }{ \sqrt{5} + \sqrt{4} } \times \frac{ \sqrt{5} - \sqrt{4} }{ \sqrt{5} - \sqrt{4} } \\ = \frac{5 - 2 \sqrt{20} + 4}{5 - 4} \\ = 9 - 2 \sqrt{20} \\ = 9 - 4 \sqrt{5}$
First of all to simplify it we will rationalize it
To rationalize an irrational number multiply the same number by it with the opposite sign for the constant term in a polynomial