Question

rationalize the denominator of the following : (i) 3 + root 2/4 root 2​

Answer 1

Answer:

$\frac{12\sqrt{2} + 8 }{8}$

Step-by-step explanation:

$\frac{3 + \sqrt{2} }{4\sqrt{2} } = \frac{3 + \sqrt{2} }{4\sqrt{2} } *\frac{4\sqrt{2} }{4\sqrt{2} } = \frac{12\sqrt{2} + 8 }{8}$

Answer 2

Answer:

The rationalised denominator is

$\boxed{\red{\sf\:\frac{3\sqrt{2}\:+\:2}{8}}}$

Step-by-step-explanation:

NOTE: Kindly refer to the attachment.

Additional Information:

1. Rationalisation of Denominator:

When the denominator of any number is a rational number, then the denominator of number is called as rationalised denominator.

The process of rationalising the denominator is called as Rationalisation of Denominator.

2. To rationalise the denominator:

To rationalise the denominator of a number, we have to multiply the number by the same denominator.

If the denominator is addiction of an irrational and rational number, then we have to use the conjugate pair of the number.

3. Conjugate Pair:

If the number is addition, the conjugate pair is subtraction.

For example,

The conjugate pair of

$\sf\:\dfrac{47}{3\sqrt{2}\:+\:2}$ is $\sf\:\dfrac{47}{3\sqrt{2}\:-\:2}$.