Question

Rationalise the denominators :16/root41 -5

Answer 1

QUESTION:-

Rationalize the denominator

$\frac{16}{ \sqrt{41} - 5 }$

Solution:-

To rationalize divide and multiply by

$\sqrt{41} + 5$

So we get

$\frac{16}{ \sqrt{41} - 5 } \times \frac{ \sqrt{41} + 5}{ \sqrt{41} + 5}$

$\frac{(16)( \sqrt{41} + 5)}{ (\sqrt{41 } - 5)( \sqrt{41} + 5) }$

Use this identities

(a-b)(a+b)=(a²-b²)

By use of this identities ,we get

$\frac{16 (\sqrt{41} + 5)}{( \sqrt{41}) {}^{2} - (5) {}^{2} }$

$\frac{16( \sqrt{41} + 5)}{41 - 25}$

$\frac{16( \sqrt{41} + 5) }{16}$

Now,

$\frac{ \not16( \sqrt{41} + 5) }{ \not16}$

We get

$\sqrt{41} + 5$

$\bf{ \large{Answer = \sqrt{41} + 5 }}$