Radical Reviews

Radical Reviews

Example 1: Simplifying Radicals

Break down the number inside the radical until you get to only prime numbers. Then for every "pair" of numbers you can take the square root and multiple it by the number outside the radical

Example 2: Simplifying Radicals

Multiple Choice

Simplify the Radical $8\sqrt{8}$  

•  $-8\sqrt{3}$  

•  $-28\sqrt{2}$  

•  $8$  

•  $16\sqrt{2}$  

Multiple Choice

Simplify the Radical $-6\sqrt{72}$  

•  $-60\sqrt{2}$  

•  $-7\sqrt{2}$  

•  $-36\sqrt{2}$  

•  $10\sqrt{2}$  

Multiple Choice

Simplify the Radical $-3\sqrt{27}$  

•  $-20$  

•  $-9\sqrt{3}$  

•  $-8\sqrt{2}$  

•  $18\sqrt{3}$  

Multiple Choice

Simplify the Radical $7\sqrt{96}$  

•  $28\sqrt{6}$  

•  $24\sqrt{2}$  

•  $-16$  

•  $-8\sqrt{105}$  

Example 3: Rationalizing the Denominator

You want to multiply the whole fraction by the square root in the denominator then simplify as much as you can.

Example 4: Rationalizing the Denominator

Multiple Choice

Simplify the radical $\frac{\sqrt{3}}{\sqrt{5}}$  

•  $\frac{\sqrt{15}}{3}$  

•  $\frac{\sqrt{15}}{5}$  

•  $\frac{5\sqrt{6}}{6}$  

•  $\frac{\sqrt{10}}{2}$  

Multiple Choice

Simplify the radical $\frac{5\sqrt{15}}{\sqrt{6}}$  

•  $\frac{4\sqrt{5}}{5}$  

•  $\frac{\sqrt{5}}{5}$  

•  $\frac{5\sqrt{10}}{2}$  

•  $\frac{\sqrt{10}}{10}$  

Multiple Choice

Simplify the radical $\frac{2}{\sqrt{5}}$  

•  $\frac{\sqrt{5}}{2}$  

•  $\frac{2\sqrt{5}}{5}$  

•  $\sqrt{15}$  

•  $\frac{5\sqrt{6}}{3}$  

Multiple Choice

Simplify the radical $\frac{\sqrt{3}}{3\sqrt{2}}$  

•  $\frac{\sqrt{5}}{15}$  

•  $\frac{\sqrt{6}}{6}$  

•  $\sqrt{6}$  

•  $\frac{4\sqrt{5}}{3}$