Reducing Radicals

​Let's practice reducing radicals that are already split up!

​The perfect square reduces!

Multiple Choice

Reduce: $$\sqrt[]{9\cdot7}$$

• $$7\sqrt[]{9}$$

• $$7\sqrt[]{3}$$

• $$3\sqrt[]{7}$$

• $$7\sqrt[]{3}$$

Multiple Choice

Reduce: $$\sqrt[]{16\cdot3}$$

• $$3\sqrt[]{16}$$

• $$16\sqrt[]{3}$$

• $$3\sqrt[]{4}$$

• $$4\sqrt[]{3}$$

Multiple Choice

Reduce: $$\sqrt[]{49\cdot6}$$

• $$6\sqrt[]{7}$$

• $$7\sqrt[]{6}$$

• $$3\sqrt[]{49}$$

• $$6\sqrt[]{49}$$

Multiple Choice

Reduce: $$\sqrt[]{5\cdot36}$$

• $$6\sqrt[]{5}$$

• $$5\sqrt[]{6}$$

• $$5\sqrt[]{36}$$

• $$36\sqrt[]{5}$$

Multiple Choice

Reduce: $$\sqrt[]{11\cdot100}$$

• $$11\sqrt[]{100}$$

• $$11\sqrt[]{10}$$

• $$10\sqrt[]{11}$$

• $$100\sqrt[]{11}$$

- To reduce square roots, you need to look for perfect squares!

​Reducing Square Roots

- Look for the numbers:

4, 9, 16, 25, 36, ........

​Reducing Square Roots

4, 9, 16, 25, 36, ..... which one is in there?

4 times 7 makes 28!

​The perfect square reduces!

Multiple Choice

When simplifying √28, which perfect square is inside of 28?

• 4

• 9

• 16

• 25

Multiple Choice

How can we rewrite √28 so that it can be reduced?

• $$\sqrt[]{4\cdot7}$$

• $$\sqrt[]{28\cdot1}$$

• $$\sqrt[]{2\cdot14}$$

Multiple Choice

What is √28 reduced?

• $$7\sqrt[]{4}$$

• $$2\sqrt[]{7}$$

• $$7\sqrt[]{2}$$

• $$4\sqrt[]{7}$$

​Let's practice that!

Multiple Choice

How can we rewrite √45 so that it can be reduced?

• $$\sqrt[]{45\cdot1}$$

• $$\sqrt[]{9\cdot5}$$

• $$\sqrt[]{3\cdot15}$$

Multiple Choice

What is √45 reduced?

• $$3\sqrt[]{15}$$

• $$5\sqrt[]{3}$$

• $$5\sqrt[]{9}$$

• $$3\sqrt[]{5}$$

Multiple Choice

How can we rewrite √50 so that it can be reduced?

• $$\sqrt[]{50\cdot1}$$

• $$\sqrt[]{10\cdot5}$$

• $$\sqrt[]{25\cdot2}$$

Multiple Choice

What is √50 reduced?

• $$5\sqrt[]{2}$$

• $$2\sqrt[]{5}$$

• $$2\sqrt[]{25}$$

• $$25\sqrt[]{2}$$

Multiple Choice

How can we rewrite √200 so that it can be reduced?

(Be careful here, we want the biggest perfect square!)

• $$\sqrt[]{25\cdot4}$$

• $$\sqrt[]{100\cdot2}$$

• $$\sqrt[]{20\cdot10}$$

• $$\sqrt[]{40\cdot5}$$

• $$\sqrt[]{200\cdot1}$$

Multiple Choice

What is √200 reduced?

• $$100\sqrt[]{2}$$

• $$2\sqrt[]{100}$$

• $$2\sqrt[]{10}$$

• $$10\sqrt[]{2}$$

Multiple Choice

How can we rewrite √32 so that it can be reduced?

(Be careful here, we want the biggest perfect square!)

• $$\sqrt[]{8\cdot4}$$

• $$\sqrt[]{16\cdot2}$$

• $$\sqrt[]{32\cdot1}$$

Multiple Choice

What is √32 reduced?

• $$4\sqrt[]{2}$$

• $$2\sqrt[]{8}$$

• $$2\sqrt[]{4}$$

• $$4\sqrt[]{8}$$

Math Response

Which perfect square would you use to reduce √63

Hint: (4, 9, 16, 25, 36, 49, ...)

Type answer here

Correct Answer: 9

Deg^°

Rad

Math Response

What is √63 reduced?

Type answer here

Correct Answer: 3\sqrt{7}

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Math Response

Which perfect square would you use to reduce √12

Hint: (4, 9, 16, 25, 36, 49, ...)

Type answer here

Correct Answer: 4

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Math Response

What is √12 reduced?

Type answer here

Correct Answer: 2\sqrt{3}

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Math Response

Which perfect square would you use to reduce √44

Hint: (4, 9, 16, 25, 36, 49, ...)

Type answer here

Correct Answer: 4

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Math Response

What is √44 reduced?

Type answer here

Correct Answer: 2\sqrt{11}

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Math Response

Which perfect square would you use to reduce √48

Hint: (4, 9, 16, 25, 36, 49, ...)

Type answer here

Correct Answer: 16

Deg^°

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Math Response

What is √48 reduced?

Type answer here

Correct Answer: 4\sqrt{3}

Deg^°

Rad