Question

6-2root5 by 6+2root5
with Simplified and step by step solution​

Answer 1

Step-by-step explanation:

simple we take LCM 6 and solve it

Answer 2

Step-by-step explanation:

Given:-

(6-2√5)/(6+2√5)

To find:-

Simplify (6-2√5)/(6+2√5)

Solution:-

Given that

(6-2√5)/(6+2√5)

Denominator = 6+2√5

We know that

The Rationalising factor of a+√b is a-√b

Now

The Rationalising factor of 6+2√5 is 6-2√5

In Rationalising the denominator then

=> [(6-2√5)/(6+2√5)]×[(6-2√5)/(6-2√5)]

=>[(6-2√5)(6-2√5)]/[(6+2√5)(6-2√5)]

=> [(6-2√5)^2]/[(6+2√5)(6-2√5)]

We know that

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

Where a = 6 and b=2√5

=> [(6-2√5)^2]/[(6)^2-(2√5)^2]

=>[(6-2√5)^2]/[36-20)]

=>[(6-2√5)^2]/(16)

We know that

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

Where a = 6 and b=2√5

=>[6^2-2(6)(2√5)+(2√5)^2]/16

=>(36-24√5+20)/16

=>(56-24√5)/16

=>8(7-3√5)/16

=>(7-3√5)/2

Answer:-

Answer for the given problem is

(6-2√5)/(6+2√5) = (7-3√5)/2

Used formulae:-

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

• (a+b)(a-b)=a^2-b^2

• (a-b)^2=a^2-2ab+b^2