1.3 Radicals and rational exponents  (Page 2/11)

1. 
   $\begin{array}{cc}\sqrt{100\cdot 3}\hfill & \text{Factor perfect square from radicand}.\hfill \\ \sqrt{100}\cdot \sqrt{3}\hfill & \text{Write radical expression as product of radical expressions}.\hfill \\ 10\sqrt{3}\hfill & \text{Simplify}.\hfill \end{array}$
2. 
   $\begin{array}{cc}\sqrt{81a^4{b}^4\cdot 2a}\hfill & \text{Factor perfect square from radicand}.\hfill \\ \sqrt{81a^4{b}^4}\cdot \sqrt{2a}\hfill & \text{Write radical expression as product of radical expressions}.\hfill \\ 9a^2{b}^2\sqrt{2a}\hfill & \text{Simplify}.\hfill \end{array}$

$\begin{array}{cc}\sqrt{12\cdot 3}\hfill & \text{Express the product as a single radical expression}.\hfill \\ \sqrt{36}\hfill & \text{Simplify}.\hfill \\ 6\hfill & \end{array}$

$\begin{array}{cc}\frac{\sqrt{5}}{\sqrt{36}}\hfill & \text{Write as quotient of two radical expressions}.\hfill \\ \frac{\sqrt{5}}{6}\hfill & \text{Simplify denominator}.\hfill \end{array}$

$\begin{array}{cc}\sqrt{\frac{234x^{11}y}{26x^{7}y}}\hfill & \text{Combine numerator and denominator into one radical expression}.\hfill \\ \sqrt{9x^4}\hfill & \text{Simplify fraction}.\hfill \\ 3x^2\hfill & \text{Simplify square root}.\hfill \end{array}$