Question

step by step explanation.
No spam​

Answer 1

First of all, we have to know about a rationalising factor. A rationalising factor is a numerical factor (or numerical surd), which can get multiplied with the given quadratic surd (here, 3+√2) to produce a pure rational number.

For example :-

$\frac{3}{ \sqrt{3} } = \frac{3 \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } = \frac{3 \sqrt{3} }{3}$

Here, in the above solution, √3 is the rationalising factor. The above process is also known as Rationalization of denominators. In certain conditions, the denominator of a fraction contains a irrational number. As per rule, we should convert that irrational number into a pure rational number. But, we will ignore if any irrational number is present in numerator.

3 + √2 is a quadratic surd. Its rationalising factors can be :

(A) 3 - √2

(B) - 3 + √2

Explanation : If we multiply these two quadratic surds with the given surd, then we will get a rational number.

Have a look :

[A] (3+√2) (3-√2) = 7, a rational number.

[B] (3+√2) (- 3 + √2) = - 7,a rational number.

Answer 2

I got the answer:-

$(3 + \sqrt{2}) \times (3 - \sqrt{2} ) \\ = > ( {3}^{2} ) - ( \sqrt{2 {}^{2} } ) \\ = > 9 - 2 \\ = > 7$