Question

Rationalise the denominator for 1
7 +3
$\sqrt{2}$
​

Answer 1

qυєsтIση :-

• Rationalise the denominator :-
• $\mathtt{ \frac{1}{7 + 3 \sqrt{2} } }$

αηsωєя :-

• $\mathtt{ \frac{1}{7 + 3 \sqrt{2} } } \\ \\ \sf{multiplying \: by \: (7 - 3 \sqrt{2}) \: in \: both } \\ \sf{numerator \: and \: denominator} \\ \\ \mathtt{ \frac{1}{7 + 3 \sqrt{2} } \times \frac{(7 - 3 \sqrt{2}) }{(7 - 3 \sqrt{2} )} } \\ \\ \mathtt{ \frac{(7 - 3 \sqrt{2}) }{(7) {}^{2} - (3 \sqrt{2} ) {}^{2} } } \\ \\ \mathtt{ \frac{7 - 3 \sqrt{2} }{49 - 18} } \\ \\ \boxed{ \mathtt{ \frac{7 - 3 \sqrt{2} }{31} }}$