Simplifying Radicals

Simplifying Radicals

Algebra 2 Live Lesson

How to simplify a radical

Simplify:

 $\sqrt{48}$  
1.  Find the largest perfect square that divides into number
2.  Rewrite square root as a product
3.  Take out perfect square and leave other number underneath radical

Multiple Choice

What is the largest perfect square that you use to simplify

 $\sqrt{24}$  

• 1

• 4

• 9

• 16

Multiple Choice

Simplify

 $\sqrt{24}$  

•  $4\sqrt{6}$  

•  $2\sqrt{6}$  

•  $6\sqrt{2}$  

•  $6\sqrt{4}$  

Multiple Choice

Simplify:

 $\sqrt{98}$  

•  $7\sqrt{2}$  

•  $2\sqrt{7}$  

•  $49\sqrt{2}$  

•  $2\sqrt{49}$  

What if you have a number on the outside?

Simplify:

 $6\sqrt{75}$  
1.  Start the same - find largest perfect square.
2.  Rewrite as a product.
3.  Take out perfect square --> MULTIPLY it by the number on the outside

Multiple Choice

Simplify:

 $10\sqrt{96}$  

•  $40\sqrt{6}$  

•  $160\sqrt{6}$  

•  $96\sqrt{10}$  

•  $60\sqrt{16}$  

Multiple Choice

Simplify:

 $3\sqrt{125}$  

•  $75\sqrt{3}$  

•  $8\sqrt{5}$  

•  $15\sqrt{5}$  

•  $15\sqrt{25}$  

What if you have variables?

1. Make sure the variable is an even power
2. If it's not even, subtract one from the exponent and rewrite as a product
3. Take the variable with the even power and divide by 2 - put that on the outside of the radical

Multiple Choice

Simplify:

 $\sqrt{x^{15}}$  

•  $x^{7.5}$  

•  $x^{14}\sqrt{x}$  

•  $x^7\sqrt{x}$  

Multiple Choice

Simplify:

 $\sqrt{x^2y^7}$  

•  $xy^3$  

•  $xy^3\sqrt{y}$  

•  $xy^3\sqrt{xy}$  

Multiple Choice

Simplify:

 $\sqrt{80x^2y^4}$  

•  $2xy^2\sqrt{20}$  

•  $4xy^2\sqrt{5}$  

Add/Subtract Radicals

Simplify:

 $\sqrt{3}+4\sqrt{27}$  
1.  Simplify all radicals
2.  You can add anything that has the same number under the radical

Multiple Choice

Simplify:

 $2\sqrt{24}+5\sqrt{54}$  

•  $7\sqrt{78}$  

•  $19\sqrt{6}$  

•  $7\sqrt{6}$  

How to Multiply Radicals

Multiply:

 $2\sqrt{5}\times3\sqrt{4}$  
1.  Multiply the coefficients
2.  Multiply the numbers under the radical
3.  Simplify radical

Multiple Choice

Multiply:

 $3\sqrt{8}\times4\sqrt{10}$  

•  $12\sqrt{80}$  

•  $7\sqrt{80}$  

•  $24\sqrt{20}$  

•  $48\sqrt{5}$