Adding and Subtracting Radicals

Multiple Choice

Simplify

$$\sqrt[]{72}$$  

• $$2\sqrt[]{6}$$  

• $$36\sqrt[]{2}$$  

• $$6\sqrt[]{2}$$  

• $$2\sqrt[]{36}$$  

• 12

Multiple Choice

Simplify:

$$\sqrt{63}$$  

• $$9\sqrt{7}$$  

• $$6\sqrt{2}$$  

• $$7\sqrt{6}$$  

• $$3\sqrt{7}$$  

​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

​Optional Video Examples of Adding and Subtracting Radicals

Optional Video #1: If you would like to watch someone explain how to add and subtract radicals, watch this first short video by clicking on the link HERE.

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Optional Video #2: If you would like to watch another explanation on how to add and subtract radicals, watch this first short video by clicking on the link HERE.

​

Some text here about the topic of discussion

Multiple Choice

Add

$$2\sqrt[]{5}+4\sqrt[]{5}$$  

• $$6\sqrt[]{10}$$  

• $$8\sqrt[]{10}$$  

• $$8\sqrt[]{5}$$  

• $$6\sqrt[]{5}$$  

Multiple Choice

Add the radicals below

$$\sqrt[]{5}+\sqrt[]{20}$$  

Hint: Simply $$\sqrt[]{20}$$ first.

• 5

• $$5\sqrt[]{5}$$  

• $$3\sqrt[]{5}$$  

• 10

Multiple Choice

Subtract the radical expressions below

$$-13\sqrt[]{11}-13\sqrt[]{11}$$  

• $$-26\sqrt[]{11}$$  

• $$-\sqrt[]{11}$$  

• $$-13\sqrt[]{11}$$  

• $$-26\sqrt[]{22}$$  

Multiple Choice

Subtract the radical expressions below

$$4\sqrt[]{12}-5\sqrt[]{27}$$  

Hint: SImplify $$\sqrt[]{12}$$ and $$\sqrt[]{27}$$ first. Look back to slide 3, if needed.

• $$-7\sqrt[]{39}$$  

• $$-7\sqrt[3]{3}$$  

• $$-\sqrt[]{15}$$  

• $$-7\sqrt[]{3}$$  

Multiple Choice

Add the radical expressions below and simplify the result.

$$9\sqrt[]{2}+12\sqrt[]{3}$$  

• $$21\sqrt[]{5}$$  

• $$21\sqrt[]{2}$$  

• $$21\sqrt[]{3}$$  

• Already simplified.  One cannot add these since the two radicands are simplified and are not exactly the same.

​If you would like to watch someone do an example of multiplying radicals, click HERE

Multiple Choice

Multiply the radical expressions and simplify the result.

$$\sqrt[]{5}\cdot\sqrt[]{10}$$  

• $$\sqrt[]{50}$$  

• $$2\sqrt[]{5}$$  

• $$5\sqrt[]{2}$$  

• 50

Multiple Choice

Multiply the radical expressions and simplify the result.

$$4\sqrt{6}\cdot\sqrt{3}$$  

• $$4\sqrt{9}$$  

• $$\sqrt{72}$$  

• $$4\sqrt{18}$$  

• $$12\sqrt{3}$$  

Multiple Choice

Multiply the radical expressions and simplify the result.

$$-3\sqrt[]{2}\cdot5\sqrt[]{3}$$  

• $$15\sqrt[]{6}$$  

• $$-15\sqrt[]{6}$$  

• $$-8\sqrt[]{6}$$  

• Already simplified

Multiple Choice

Multiply and simplify:

$$\sqrt[]{6}\cdot\sqrt[]{6}$$  

• $$\sqrt[]{36}$$  

• $$2\sqrt[]{3}$$  

•   $$\sqrt[]{6}$$  

• 6

Multiple Choice

Multiply and simplify

$$\sqrt[]{3}\cdot\sqrt[]{15}$$  

• $$3\sqrt[]{5}$$  

• $$5\sqrt[]{3}$$  

•   $$9\sqrt[]{5}$$  

• $$\sqrt[]{45}$$