Question

6/√8-3 rationalize the following​

Answer 1

6/root 8+3 × root 8-3

6(root 8-3)/(root 8^2)

Answer 2

Given:

The expression -

$\bf \dashrightarrow \dfrac{6}{\sqrt{8} - 3}$

What To Find:

We have to -

• Rationalise the denominator.

How To Find:

To find we have to -

• First, find the rationalising factor of the denominator.
• Next, multiply the rationalising factor with the expression.
• Solve, the expressions using identities.

Solution:

Here, the rationalising factor of the denominator is,

$\sf \implies \sqrt{8} + 3$

Multiply the rationalising factor with the expression,

$\sf \implies \dfrac{6}{\sqrt{8} - 3} \times \dfrac{\sqrt{8} + 3}{\sqrt{8} + 3}$

Take them as common,

$\sf \implies \dfrac{6 \times \sqrt{8} + 3 }{\sqrt{8} - 3 \times \sqrt{8} + 3}$

Solve the numerator,

$\sf \implies \dfrac{6\sqrt{8} + 18 }{\sqrt{8} - 3 \times \sqrt{8} + 3}$

Solve the denominator using the identity (a + b) (a - b) = a² - b²,

Where,

• a = √8
• b = 3

$\sf \implies \dfrac{6\sqrt{8} + 18 }{(\sqrt{8})^2 - (3)^2}$

Find the squares,

$\sf \implies \dfrac{6\sqrt{8} + 18 }{8 - 9}$

Subtract 9 from 8,

$\sf \implies \dfrac{6\sqrt{8} + 18 }{-1}$

Also written as,

$\sf \implies - 6\sqrt{8} + 18$

Final Answer:

∴ Thus, the answer is - 6√8 + 18 after rationalising the denominator of the expression.