Question

Rationalize the denominator and simplify to find the value of:
4/root5+root3
Given that root5=2.236 and root3=1.732

Answer 1

2√5.2√3 will be the answer. substitute those root values.

Answer 2

Therefore $\frac{4}{\sqrt5+\sqrt3} =1.008$

Step-by-step explanation:

Given that,

$\frac{4}{\sqrt5+\sqrt3}$

$=\frac{4(\sqrt5-\sqrt3)}{(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)}$   [ multiply the numerator and denominator by $(\sqrt5-\sqrt3)$]

$=\frac{4(\sqrt5-\sqrt3)}{(\sqrt5)^2-(\sqrt3)^2}$          [ Applying the formula (a+b)(a-b)=a²-b²]

$=\frac{4(\sqrt5-\sqrt3)}{5-3}$              [ $\because (\sqrt x)^2=x$  ]

$=\frac{4(\sqrt5-\sqrt3)}{2}$

$={2(\sqrt5-\sqrt3)}$

Given $\sqrt5 =2.236$  and  $\sqrt3=1.732$

Putting the value of $\sqrt5$ and $\sqrt3$

=2(2.236-1.732)

=2(0.504)

=1.008

Therefore $\frac{4}{\sqrt5+\sqrt3} =1.008$