Simplifying Radicals

Simplifying Radicals

Solving by taking Square Roots

Multiple Choice

Which of the following is a perfect square?

• $\sqrt{8}$

• $\sqrt{49}$

• $\sqrt{18}$

• $\sqrt{125}$

To Simplify a Square Root is the process of evaluating the perfect squares that are factors.

For example:

 $\sqrt{8}=\sqrt{4}\times\sqrt{2}$  

 $\sqrt{8}=2\sqrt{2}$  

Multiple Choice

Simplifying a Square Root:

 $\sqrt{perfect\ square}\times\sqrt{non\ perfect\ square}$   $example:\ \ \sqrt{45}$  

•  $9\sqrt{5}$  

•  $5\sqrt{9}$  

•  $3\sqrt{5}$  

•  $5\sqrt{3}$  

Multiple Choice

 $Simplify:\ \ \sqrt{20}$ 
 

•  $2\sqrt{10}$  

•  $4\sqrt{5}$  

•  $10\sqrt{2}$  

•  $2\sqrt{5}$  

Solving Quadratics by taking Square Roots:

Solve (there will be two solutions):
 $\left(x+3\right)^2=100$  

 $\left(x+6\right)^2=45$  

Answer should be in simplified radical form.

Multiple Select

 $Solve:\ \left(x-8\right)^2=28$  
Next steps:

• Square both sides

• Take the square root of both sides

Multiple Select

 $\sqrt{\left(x-8\right)^2}=\sqrt{28}$  

•  $x^2-64=14$  

•  $x-8=\pm\sqrt{28}$  

Multiple Select

 $x-8=\pm\sqrt{28}$  

•  $x=8\pm4\sqrt{7}$  

•  $x=8\pm7\sqrt{2}$  

•  $x=8\pm2\sqrt{7}$  

•  $x=-8\pm2\sqrt{7}$