### Home > PC3 > Chapter Ch8 > Lesson 8.3.2 > Problem8-101

8-101.

Rewrite each expression below.

1. $(5-\sqrt { 3 })(5+\sqrt {3})$

$5^2+5\sqrt{3}-5\sqrt{3}-\sqrt3^2$

1. $(\sqrt{6}+\sqrt{2})(\sqrt{6}-\sqrt{2})$

$\sqrt{6}^2-\sqrt{6}\sqrt{2}+\sqrt{6}\sqrt{2}-\sqrt{2}^2$

Recall that rationalizing a denominator means to rewrite a fraction so that there are no irrational numbers in the denominator. Look at the expressions in parts (a) and (b). What do you notice? Use this pattern to rationalize each of the following denominators.

1. $\frac { 4 } { 5 - \sqrt { 3 } }$

$\frac{4}{5-\sqrt{3}}\cdot\frac{5+\sqrt{3}}{5+\sqrt{3}}$

1. $\frac { 1 + \sqrt { 3 } } { \sqrt { 6 } + \sqrt { 2 } }$

$\frac{1+\sqrt{3}}{\sqrt{6}+\sqrt{2}}\cdot\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}-\sqrt{2}}$