Question

Rationalise the denominator a)1/2+root3 b)5/root3-root 5 c)1/3root2

Answer 1

1) 1/2+√3=1/2+√3*2-√3/2-√3
2-√3/ 2^2-√3^2 . (a+B)(a-b)=a^2-b^2

2-√3/4-3

2-√3/1

2-√3


2) √3/√5=√3/√5*√5/√5

then

=√15/√25

=√15/√25*√/√
then

=15/25

=3/5

3) I think it's answer is 1/3√2

Answer 2

Following are the answers :

a. 1 / 2 + √ 3 × 2 - √ 3 / 2 - √ 3

= 1 ( 2 - √ 3 ) / ( 2 + √ 3 ) ( 2 - √ 3 )

= 2 - √ 3 / ( 2 ) ^ 2 - ( √ 3 ) ^ 2

= 2 - √ 3 / 4 - 3

= 2 - √ 3 / 1

= 2 - √ 3.

b. 5 / √ 3 - √ 5 × √ 3 + √ 5 / √ 3 + √ 5

= 5 ( √ 3 + √ 5 ) / [ (√ 3 ) ^ 2 - ( √ 5 ) ^ 2

= 5 ( √ 3 + √ 5 ) / 3 - 5

= 5 ( √ 3 + √ 5 ) / - 2.

c. 1 / 3 √ 2

= 1 ( 3 - √ 2 ) / ( 3 √ 2 ) ^ 2

= 3 √ 2 / 18

= √ 2 / 6.

[ I WOULD HAVE POSTED THE PICTURE BUT MY CAMERA ISN'T WORKING ]…

ANYWAYS..

HOPE IT HELPED.. :))