Question

rationalize 1 upon - 3 + root 7​

Answer 1

Rationalize $\frac{1}{-3+\sqrt{7} }$

Key : Use identity $(a+b)(a-b)=a^2-b^2$ on denominator.

$\frac{1}{-3+\sqrt{7} }=\frac{-3-\sqrt{7} }{(-3+\sqrt{7} )\times (-3-\sqrt{7} )}=\frac{-3-\sqrt{7}}{(-3)^2-7}=-\frac{3+\sqrt{7} }{2}$

The answer is $-\frac{3+\sqrt{7} }{2}$.