Question

rationalise the denominator by 5+√ 3/7+4√ 3

Answer 1

35-13√3-12 / 61. is answer

Answer 2

Answer:

$23-13\sqrt{3}$

Step-by-step explanation:

To rationalise the denominator, the main tip to remember is its rationalising factor or its conjugate.

The denominator of$\frac{5+\sqrt{3} }{7+4\sqrt{3} }$ is 7 +4√3

Hence the conjugate is 7-4√3.

Multiplying the numerator and the denominator by the conjugate,  7-4√3,

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

=$\frac{35+7\sqrt{3}-20\sqrt{3} -12}{(7)^{2}-(4\sqrt{3)^{2} }  }$

=$\frac{23-13\sqrt{3} }{49-48}$

=$\frac{23-13\sqrt{3} }{1}$

Thus the denominator is 1, which is rational.

Hence the denominator has been rationalised.

Hope it helped you.

Do mark this answer as the brainliest.

Follow me to get all your maths doubts cleared