Question

rationilice the demoninator 5 by root 3 -root 5

Answer 1

Answer:

$\frac{5 \sqrt{3} + 5 \sqrt{5} }{ - 2}$

Step-by-step explanation:

so rationalising means if the denominator is irrational we convert it into a rational number

we rationalise a number to make the calculations easier

and to rationalise a number we use the property of equivalent fraction

so here.

$\frac{5}{ \sqrt{3} - \sqrt{5} }$

we will multiply both numerator and denominator by √3 +√5

now you will ask why

because if we multiply root 3 by root 3 it will give root 3 square also can be written as 3

so here you can see how we convert a irrational number into a rational number

the same case is with root 5 also

if we multiply root 5 by root 5 it will give root 5 square also can be written as 5

now you will ask why you change the sign - Into+

because if we will left with minus sign then you have to apply( a+b)^2 =a^2 -2ab+b^2 and in this formula we will left with 2ab

so we apply (a+b)(a-b)= a^2-b^2 this formula

now solve the question

$\frac{5}{ \sqrt{3} - \sqrt{5} } \times \frac{ \sqrt{3} + \sqrt{5} }{ \sqrt{3} + \sqrt{5} } \\ = \frac{5 \sqrt{3} + 5 \sqrt{5} }{ { \sqrt{3} }^{2} - { \sqrt{5} }^{2} } = \\ \frac{5 \sqrt{3} + 5 \sqrt{5} }{ 3 - 5} = \frac{5 \sqrt{3} + 5 \sqrt{5} }{ - 2}$

so this is your answer mark me brainliest

Answer 2

Answer:

Step-by-step explanation: