Question

x minus y divided / root x minus root y​

Answer 1

Step-by-step explanation:

Given :-

x minus y divided / root x minus root y

To find:-

Find the value of the given expression

Solution:-

Method-1:-

Given that

x minus y divided / root x minus root y

=> (x-y)/(√x -√y)

Denominator = √x -√y

Rationalising factor of√x-√y = √x+√y

On Rationalising the denominator then

=> [(x-y)/(√x-√y) ]×[(√x+√y)/(√x+√y)]

=> [(x-y)(√x+√y)]/[(√x-√y)(√x+√y)]

We know that

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

=> [(x-y)(√x+√y)/[(√x)^2-(√y)^2]

=> [(x-y)(√x+√y)]/(x-y)

=> √x+√y

Method-2:-

Given that

(x-y)/(√x -√y)

It can be written as

=> [(√x)^2-(√y)^2]/(√x-√y)

We know that

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

=> [(√x+√y)(√x-√y)]/(√x-√y)

=> √x +√y

Answer:-

The value of the given problem (x-y)/(√x -√y) is

√x +√y

Used formulae:-

• (a+b)(a-b)=a^2-b^2

• The product of two irrational numbers is a rational number then the two numbers are called Rationalising factors of each other.

• The Rationalising factor of√a-√b = √a+√b