Question

The rationalising factor for the number $3-7\sqrt{2}$ is

• A. $3+2\sqrt{7}$
• B. $-3-2\sqrt{7}$
• C. $3+7\sqrt{2}$
• D. $-3+7\sqrt{2}$

Answer 1

The correct option is C

$3+7\sqrt{2}$

We know that $(a+b)(a-b)=a^2-b^2$
Now, if an expression of the form $(a\sqrt{b}+c\sqrt{d})$ is given, we can rationalise that expression by multiplying it with $(a\sqrt{b}-c\sqrt{d})$ since
$(a\sqrt{b}+c\sqrt{d})(a\sqrt{b}-c\sqrt{d})=a^{2}b-c^{2}d$
Thus, to rationalise $(3-7\sqrt{2})$, we multiply it with $3+7\sqrt{2}$.
The expression that is multiplied with an irrational expression to obtain a rational number is called the "rationalising factor".