A.3 Radicals

Simplifying Radicals

How to simplify a radical

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?

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

Multiple Choice

Simplify:

$$2\sqrt{24}+5\sqrt{54}$$  

• $$7\sqrt{78}$$  

• $$19\sqrt{6}$$  

• $$7\sqrt{6}$$  

Multiple Choice

Simplify $$\sqrt{56}$$  

• $$2\sqrt{14}$$  

• $$4\sqrt{14}$$  

• $$2\sqrt{28}$$  

• $$2\sqrt{9}$$  

Multiple Choice

Simplify. $$\sqrt{28m}$$  

• $$2\sqrt{7m}$$  

• $$2\sqrt{2\cdot7m}$$  

• $$7\sqrt{2m}$$  

• $$2m\sqrt{7}$$