Adding and Subtracting Square Roots

Adding and Subtracting Square Roots

Unit 1

Square Root Review

Definition : The square root of a positive number is the number when multiplied by itself, equals to the given number.

Examples:

 $\sqrt{4}=\sqrt{2\times2}=2$  
 $\sqrt{9}=\sqrt{3x3}=3$  

Adding and Subtracting Square Roots

Rules
1. You can only add and subtract roots of the same number. $\sqrt{2}+\sqrt{2}\ is\ ok\ \ \ \ \ \ \ \ \ \ \sqrt{2}+\sqrt{3}\ is\ not\ ok$  

2. You add and subtract the amount in front of the square root.
 $3\sqrt{5}+4\sqrt{5}=7\sqrt{5}$  

3. If there is no number in front of a square root, that counts as 1 square root.

 $\sqrt{2}=1\sqrt{2}\ \ \ \ \ so\ \ \ \ \sqrt{2}+4\sqrt{2}=5\sqrt{2}$  

Multiple Choice

$$5\sqrt{5}+2\sqrt{5}=?$$  

• $$7\sqrt{10}$$  

• $$7\sqrt{5}$$  

• $$10\sqrt{5}$$  

• $$7\sqrt{25}$$  

Multiple Choice

$$8\sqrt{2}-3\sqrt{2}$$  

• $$5\sqrt{2}$$  

• $$5\sqrt{4}$$  

• $$11\sqrt{2}$$  

Multiple Choice

$$\sqrt{7}+7\sqrt{7}-2\sqrt{7}$$  

• $$5\sqrt{7}$$  

• $$6\sqrt{7}$$  

• $$8\sqrt{7}$$  

• $$9\sqrt{7}$$  

Multiple Choice

$$3\sqrt{2}+2\sqrt{3}$$  

• $$6\sqrt{6}$$  

• $$5\sqrt{5}$$  

• $$3\sqrt{2}+2\sqrt{3}$$  

• $$5\sqrt{2}$$