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Algebra II : Multiplying and Dividing Radicals

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Example Question #21 : Multiplying And Dividing Radicals

Simply this radical: $\sqrt{6}\sqrt{8}\sqrt{10}$

Possible Answers:

$\sqrt{30}$

None of the other answers.

$4\sqrt{30}$

$2\sqrt{30}$

$4\sqrt{15}$

Correct answer:

$4\sqrt{30}$

Explanation:

If you do not immediately see a perfect square within a number then break it down into smaller numbers. Then select from those a perfect square to be removed. When multiplying radicals it is easiest to start by combining them all under one radical.

$\sqrt{6}\sqrt{8}\sqrt{10}$

combine under one roof:

$\sqrt{6*8*10}$

now break apart each number into its factors

$\sqrt{2*3*2*2*2*5}$ now you can see perfect squares that were otherwise not there. Remove perfect squares. For example two 2's makes 4 which is a perfect square...

$4\sqrt{2*3*5}$

simplify under the radical

$4\sqrt{30}$

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Example Question #211 : Radicals

Simplify.

$\sqrt{2}(\sqrt{3}-\sqrt{5})$

Possible Answers:

$5\sqrt{3}$

$3\sqrt{5}$

$\sqrt{6}-\sqrt{10}$

$2\sqrt{10}$

Correct answer:

$\sqrt{6}-\sqrt{10}$

Explanation:

$\sqrt{2}(\sqrt{3}-\sqrt{5})$ Distribute. When multiplying radicals, you can combine them and multiply the numbers inside the radical.

$\sqrt{6}-\sqrt{10}$

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Example Question #23 : Multiplying And Dividing Radicals

Multilpy and simplify: $\sqrt{12x}\cdot \sqrt{3x^2y}$

Possible Answers:

$x\sqrt{xy}$

$6x\sqrt{y}$

$6x\sqrt{x}$

$6x\sqrt{xy}$

$6\sqrt{xy}$

Correct answer:

$6x\sqrt{xy}$

Explanation:

Multiply and simplify: $\sqrt{12x}\cdot \sqrt{3x^2y}$ . I like to multiply everything and put it all underneath one big radical first: $\sqrt{36x^3y}$ . Then, simplify each term separately. factors to $3\cdot 3\cdot 2\cdot 2$ . When dealing with square roots, for every pair of the same number, you cross the pair out and put one of those numbers outside of the radicals. The loners remain underneath the radical. Therefore, $\sqrt{36}=6$ . Do the same with the and terms. Therefore, your answer is: $6x\sqrt{xy}$ .

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Example Question #21 : Multiplying And Dividing Radicals

Simplify.

$\frac{\sqrt{12}}{\sqrt{6}}$

Possible Answers:

$\frac{3\sqrt{2}}{2}$

$\sqrt{6}$

$\frac{2\sqrt{3}}{3}$

$\sqrt{2}$

Correct answer:

$\sqrt{2}$

Explanation:

When dividing radicals, we can try to simplify it by combining the radicals.

$\frac{\sqrt{12}}{\sqrt{6}}=\sqrt{\frac{12}{6}}=\sqrt{2}$

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Example Question #23 : Multiplying And Dividing Radicals

Simplify.

$\frac{\sqrt{24}}{\sqrt{2}}$

Possible Answers:

$2\sqrt{3}$

$3\sqrt{2}$

$\frac{2\sqrt{3}}{3}$

$\frac{3\sqrt{2}}{2}$

Correct answer:

$2\sqrt{3}$

Explanation:

When dividing radicals, we can try to simplify it by combining the radicals.

$\frac{\sqrt{24}}{\sqrt{2}}=\sqrt{\frac{24}{2}}=\sqrt{12}=2\sqrt{3}$ Remember to factor out the square and that's how you can complete the simplification.

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Example Question #121 : Simplifying Radicals

Simplify.

$\sqrt{5}\cdot\sqrt{2}$

Possible Answers:

$\sqrt{10}$

$2\sqrt{5}$

$5\sqrt{2}$

$\sqrt{7}$

Correct answer:

$\sqrt{10}$

Explanation:

When multiplying radicals, you can combine them and multiply the numbers inside the radical.

$\sqrt{5}\cdot\sqrt{2}=\sqrt{5\cdot2}=\sqrt{10}$

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Example Question #27 : Multiplying And Dividing Radicals

Simplify.

$\sqrt{6}\cdot3\sqrt{6}$

Possible Answers:

$4\sqrt{6}$

$6\sqrt{3}$

Correct answer:

Explanation:

$\sqrt{6}\cdot3\sqrt{6}$ When multiplying radicals, you can combine them and multiply the numbers inside the radical. NUmbers outside the radical are also multiplied.

$3\sqrt{36}$ We can simplify this.

$3\cdot6=18$

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Example Question #21 : Multiplying And Dividing Radicals

Simplify.

$\sqrt{6}\cdot\sqrt{3}$

Possible Answers:

$2\sqrt{3}$

$3\sqrt{2}$

$\sqrt{18}$

$9\sqrt{2}$

Correct answer:

$3\sqrt{2}$

Explanation:

$\sqrt{6}\cdot\sqrt{3}$ When multiplying radicals, you can combine them and multiply the numbers inside the radical.

$\sqrt{18}$ We can simplify this. Lets find a perfect square.

$\sqrt{18}=\sqrt{9}\cdot\sqrt{2}=3\sqrt{2}$

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Example Question #29 : Multiplying And Dividing Radicals

Simplify.

$\frac{\sqrt{24}}{4}$

Possible Answers:

$\frac{\sqrt{6}}{2}$

$\frac{\sqrt{6}}{4}$

$\frac{\sqrt{2}}2{}$

$\frac{\sqrt{24}}4{}$

Correct answer:

$\frac{\sqrt{6}}{2}$

Explanation:

When dividing radicals with an integer, let's simplify the radical. We need to find a perfect square.

$\frac{\sqrt{24}}{4}=\frac{\sqrt{4}\cdot\sqrt{6}}{4}=\frac{2\sqrt{6}}{4}$ . We can reduce.

$\frac{2\sqrt{6}}{4}=\frac{\sqrt{6}}{2}$

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Example Question #30 : Multiplying And Dividing Radicals

Simplify.

$\frac{\sqrt{48}}{16}$

Possible Answers:

$\frac{\sqrt{3}}4{}$

$4\sqrt{3}$

$2\sqrt{3}$

$\sqrt{3}$

$\frac{\sqrt{3}}{2}$

Correct answer:

$\frac{\sqrt{3}}4{}$

Explanation:

When dividing radicals with an integer, let's simplify the radical. We need to find a perfect square.

$\frac{\sqrt{48}}{16}=\frac{\sqrt{16}\cdot\sqrt{3}}{16}=\frac{4\sqrt{3}}{16}$ . We can reduce.

$\frac{4\sqrt{3}}{16}=\frac{\sqrt{3}}{4}$

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Algebra II : Multiplying and Dividing Radicals

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #21 : Multiplying And Dividing Radicals

Example Question #211 : Radicals

Example Question #23 : Multiplying And Dividing Radicals

Example Question #21 : Multiplying And Dividing Radicals

Example Question #23 : Multiplying And Dividing Radicals

Example Question #121 : Simplifying Radicals

Example Question #27 : Multiplying And Dividing Radicals

Example Question #21 : Multiplying And Dividing Radicals

Example Question #29 : Multiplying And Dividing Radicals

Example Question #30 : Multiplying And Dividing Radicals

All Algebra II Resources

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