Which of the following is the rationalising factor of 3−7√2
3 + 7√2
We know that (a+b)(a−b)=a2−b2
Now, if an expression of the form (a√b+c√d) is given, we can rationalise that expression by multiplying it with (a√b−c√d) since
(a√b+c√d)(a√b−c√d)=a2b−c2d
Thus, to rationalise (3−7√2), we multiply it with 3+7√2.
The expression that is multiplied with an irrational expression to obtain a rational number is called the "rationalising factor".