Question

2 root 2 + 3 / 2 root 3 - 2

Answer 1

Answer:

Since we have given that

\frac{3-2\sqrt{2}}{3+2\sqrt{2}}

3+2

2

3−2

2

We need to rationalise the denominator:

So, we will multiply 3-2√2 by both the numerator and denominator.

So, it becomes,

\begin{gathered}\dfrac{3-2\sqrt{2}\times (3-2\sqrt{2})}{(3+2\sqrt{2})\times (3-2\sqrt{2})}\\\\=\dfrac{9+8-12\sqrt{2}}{9-8}\\\\=17+12\sqrt{2}\end{gathered}

(3+2

2

)×(3−2

2

)

3−2

2

×(3−2

2

)

=

9−8

9+8−12

2

=17+12

2

Hence, after rationalisation, we get that 17+12√2.