Question

Rationalise 5+root 3 by 7+4 root 3

Answer 1

Hi there

Your answer is :-

$\frac{5 + \sqrt {3}}{7+4\sqrt{3}}$

$(5+\sqrt{3})\times(7-4\sqrt{3})$

$35-20\sqrt{3}+7\sqrt{3}-12$

$23-13\sqrt{3} ( Ans )$


Thank You

Answer 2

Hi ,

5 + √3 / 7 + 4√3

We know that, Rationalising factor of 7 + 4√3 is it's conjugate ,

R. F of 7 + 4√3 = 7 - 4√3

So,

$\frac{5 + \sqrt 3 }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} }$

= [ 5 ( 7 - 4√3 ) + √3 ( 7 - 4√3 ) ] / 49 - 4(3)

= 35 - 20√3 + 7√3 - 12 / 49 - 12

= 23 - 13 √3 / 37

We know that ...

A fraction remains the same if it is multiplied by same number in numerator and denominator.

Also, a² - b² = ( a + b) ( a - b)

Hope helped!