Question

Which of the following is simplest rationalising factor of root 147

Answer 1

Given data:

The number $\sqrt{147}$

To find:

The simplest rationalising factor of $\sqrt{147}$

Step-by-step explanation:

First we factorise the number $147$

• $147=3\times 49$
• $147=3\times 7\times 7$

We see that $3$ comes once and $7$ comes twice. So when we take the square root of $147$, $7$ can come out of the root, but not $3$

$\Rightarrow \sqrt{147}=\sqrt{3\times 7\times 7}$

$\Rightarrow \sqrt{147}=7\sqrt{3}$,

Answer:

Hence the simplest rationalising factor of $\sqrt{147}$ is $7\sqrt{3}$.