Question

rationalise the equation
plz do it fastly and who will answer first I will mark as brainlest
do not give irrelevant answer ​

Answer 1

Question:-

• 1 + √2 / 3 + 2√2

Answer:-

• 1 + √2 / 3 + 2√2

• Rationalising factor of 3 + 2√2 is 3 - 2√2

• Multiply 3 - 2√2 with numerator and denominator.

• 1 + √2 * 3 - 2√2 / 3 + 2√2 * 3 - 2√2

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

• 3 - 2√2 + 3√2 - 4 / 9 - 6√2 + 6√2 - 8

• Rearranging the terms in numerator and denominator

• 3 - 4 + 3√2 - 2√2 / 9 - 8 + 6√2 - 6√2

• 3 - 8 = - 1 and + 3√2 - 2√2 = √2 and 9 - 8 = 1 and + 6√2 - 6√2 = 0

• - 1 + √2 / 1

• - 1 + √2

Conclusion:-

• Therefore, 1 + √2 / 3 + 2√2 = - 1 + √2.

Answer 2

$\Large{\underbrace{\underline{\bf{QUESTION\:}}}}:$

Rationalise the following equation.

$\dagger\:\bf\red{\dfrac{1\:+\:\sqrt{2}}{3\:+\:2\sqrt{2}}\:}$

$\Large{\underbrace{\underline{\bf{ANSWER\:}}}}:$

$:\implies\:\tt{\dfrac{1\:+\:\sqrt{2}}{3\:+\:2\sqrt{2}}\:}$

$:\implies\:\tt{\dfrac{(1\:+\:\sqrt{2})\:(3\:-\:2\sqrt{2})}{(3\:+\:2\sqrt{2})\:(3\:-\:2\sqrt{2})}\:}$

$:\implies\:\tt{\dfrac{3\:-\:2\sqrt{2}\:+\:3\sqrt{2}\:-\:(2\sqrt{2}\times{\sqrt{2}})}{3^2\:-\:(2\sqrt{2})^2}\:}$

$:\implies\:\tt{\dfrac{3\:+\:\sqrt{2}\:-\:(2\times{2})}{9\:-\:(4\times{2})}\:}$

$:\implies\:\tt{\dfrac{3\:+\:\sqrt{2}\:-\:4}{9\:-\:8}\:}$

$:\implies\:\tt{\dfrac{\sqrt{2}\:-\:1}{1}\:}$

$:\implies\:\bf\green{(\sqrt{2}\:-\:1)\:}\:\:(Answer)$