Question

rationalise the denominator of 31/7+3√2

Answer 1

Pls mark as brainliest answer

Answer 2

Answer :

7 - 3 √2

Given :

• $\bf \dfrac{31}{7+3\sqrt{2} }$

To Find :

• To rationalize the denominator.

Solution :

$\bf \dfrac{31}{7+3\sqrt{2} }$

Now the rationalizing factor of 7+3√2  is  7-3√2

$\implies \bf \dfrac{31}{7+3\sqrt{2} }*\dfrac{7-3\sqrt{2} }{7-3\sqrt{2} }\\\\\implies \bf \dfrac{31(7-3\sqrt{2})}{7^2-(3\sqrt{2})^2}\;[\;Since,(a+b)(a-b)=a^2-b^2]\\\\\implies \bf \dfrac{31(7-3\sqrt{2})}{49-18}\\\\\implies \bf \dfrac{31(7-3\sqrt{2})}{31}\\\\\implies \underline {\bf 7-3\sqrt{2}}$

More Info :

• Rationalizing factor(R.f) of a+k√b is a-k√b

• while solving this type of questions or else while rationalizing we need to multiply both denominator and numerator with R.f