Adding and Subtracting Radicals

​Radicals can be added/subtracted if they have the same radicand as shown above. This is very similar to adding/subtracting terms with like variables...

2x + 3x = 5x or 7x - 4x = 3x or 6x + 3x + 2y = 9x + 2y

Add/Subtract Radicals

Multiple Choice

I can simplify radical expressions that include addition and subtraction.

Simplify the radical expression below.

$$\sqrt{175}-\sqrt{28}=$$  

• $$21\sqrt{7}$$  

• $$3\sqrt{7}$$  

• $$7\sqrt{7}$$  

Multiple Choice

Simplify

$$3^{\ \ 3}\sqrt{54}-2^{\ \ 3}\sqrt{2}+7^{\ \ 3}\sqrt{-16}$$  

• $$-7^{\ \ 3}\sqrt{2}$$  

• $$3^{\ \ 3}\sqrt{2}-2^{\ \ 3}\sqrt{2}-14$$  

• $$9^{\ \ 3}\sqrt{2}-2^{\ \ 3}\sqrt{2}-14^{\ \ 3}\sqrt{2}$$  

Multiple Choice

$$2+2\sqrt[]{2}+\sqrt[]{8}+3\sqrt[]{2}$$  

• $$2+7\sqrt[]{2}$$  

• $$2+\sqrt[]{8}+7\sqrt[]{2}$$  

• $$2+7\sqrt[]{10}$$  

• $$\sqrt[]{8}+9\sqrt[]{2}$$  

Multiple Choice

Simplify  $$10\sqrt{28}-^3\sqrt{-56}-4\sqrt{175}$$  

• $$-2\sqrt{7}$$  

• $$-2^{\ \ 3}\sqrt{7}$$  

• $$-22^{\ \ 3}\sqrt{7}$$  

Multiple Choice

Simplify 
3√6 - 4√6

• -√6

• √6

• -1

• Already simplified 

Multiple Choice

Simplify 
-10√7 + 12√7

• -2

• -2√7

• 2√7

• Already simplified