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Algebra II : Radicals

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Example Questions

Example Question #142 : Simplifying Radicals

$3\sqrt{3}*\sqrt{8}$

Possible Answers:

$3\sqrt{24}$

$3\sqrt{6}$

$6\sqrt{6}$

$3\sqrt{24}$

Correct answer:

$6\sqrt{6}$

Explanation:

$3\sqrt{3}*\sqrt{8}$

Combine radicals:

$3\sqrt{24}$

Simplify the radical leftover:

$3\sqrt{6*4}$

$\mathbf{6\sqrt{6}}$

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Example Question #241 : Radicals

Divide and simplify: $\frac{28\sqrt{24}}{7\sqrt{6}}$

Possible Answers:

None of these

$4\sqrt{6}$

Correct answer:

Explanation:

$\frac{28\sqrt{24}}{7\sqrt{6}}$

Divide outside number:

$\frac{4\sqrt{24}}{\sqrt{6}}$

Divide radicals:

$4\sqrt{4}$

Simplify radical:

$4*2=\mathbf{8}$

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Example Question #42 : Multiplying And Dividing Radicals

Expand, then simplify: $(\sqrt{6}+9)^2$

Possible Answers:

$87+18\sqrt{6}$

$87+6\sqrt{18}$

$87+\sqrt{6}$

$87+6\sqrt{18}$

$87+18\sqrt{6}$

$87+6\sqrt{18}$

$87+18\sqrt{6}$

Correct answer:

$87+18\sqrt{6}$

Explanation:

$(\sqrt{6}+9)^2$

$(\sqrt{6}+9)^2=(\sqrt{6}+9)(\sqrt{6}+9)$

Foil:

$6+9\sqrt{6}+9\sqrt{6}+81$

$\mathbf{87+18\sqrt{6}}$

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Example Question #151 : Simplifying Radicals

Simplify:

$\sqrt{6}*\sqrt{8}$

Possible Answers:

$4\sqrt{3}$

$2\sqrt{6}$

$4\sqrt{2}$

$4\sqrt{6}$

$2\sqrt{3}$

Correct answer:

$4\sqrt{3}$

Explanation:

$\sqrt{6}*\sqrt{8}$ Multiply the numbers inside the radical.

$\sqrt{6}*\sqrt{8}=\sqrt{6*8}=\sqrt{48}$ Factor out a perfect square of .

$\sqrt{48}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$

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Example Question #4142 : Algebra Ii

Simplify:

$\sqrt{14}*\sqrt{21}$

Possible Answers:

$7\sqrt{6}$

$7\sqrt{2}$

$21\sqrt{3}$

$49\sqrt{3}$

$14\sqrt{2}$

Correct answer:

$7\sqrt{6}$

Explanation:

$\sqrt{14}*\sqrt{21}$ Multiply the numbers inside the radical.

$\sqrt{14}*\sqrt{21}=\sqrt{14*21}=\sqrt{294}$ Factor out a perfect square of .

$\sqrt{294}=\sqrt{49}*\sqrt{6}=7\sqrt{6}$

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Example Question #241 : Radicals

Simplify:

$\frac{\sqrt{338}}{\sqrt{169}}$

Possible Answers:

$\sqrt{3}$

$\sqrt{2}$

$\frac{1}{2}$

Correct answer:

$\sqrt{2}$

Explanation:

$\frac{\sqrt{338}}{\sqrt{169}}$ Divide the numbers inside the radicals.

$\frac{\sqrt{338}}{\sqrt{169}}=\sqrt{\frac{338}{169}}=\sqrt{2}$

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Example Question #242 : Radicals

Simplify:

$\sqrt{7}*\sqrt{5}$

Possible Answers:

$5\sqrt{7}$

$2\sqrt{3}$

$7\sqrt{5}$

$\sqrt{35}$

$\sqrt{57}$

Correct answer:

$\sqrt{35}$

Explanation:

When multiplying radicals, simply multiply the numbers inside the radical with each other. Therefore:

$\sqrt{7}*\sqrt{5}=\sqrt{35}$

We cannot further simplify because both of the numbers multiplied with each other were prime numbers.

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Example Question #51 : Multiplying And Dividing Radicals

Simplify:

$\sqrt{8}*\sqrt{10}$

Possible Answers:

$16\sqrt{5}$

$\sqrt{80}$

$4\sqrt{5}$

$5\sqrt{6}$

$6\sqrt{10}$

Correct answer:

$4\sqrt{5}$

Explanation:

When multiplying radicals, simply multiply the numbers inside the radical with each other. Therefore:

$\sqrt{8}*\sqrt{10}=\sqrt{80}$

We can simplify this by factoring and finding perfect perfect squares.

$\sqrt{80}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$

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Example Question #52 : Multiplying And Dividing Radicals

Simplify:

$2\sqrt{3}*\sqrt{6}$

Possible Answers:

$2\sqrt{18}$

$4\sqrt{6}$

$6\sqrt{6}$

$3\sqrt{2}$

$6\sqrt{2}$

Correct answer:

$6\sqrt{2}$

Explanation:

When we multiply expressions containing both radicals and whole numbers, we simply multiply the numbers inside the radical with each other and those outside the radical with each other.

$2\sqrt{3}*\sqrt{6}=2\sqrt{18}$ .

We can simplify this by factoring and finding perfect perfect squares.

$2\sqrt{18}=2*\sqrt{9}*\sqrt{2}=2*3*\sqrt{2}=6\sqrt{2}$

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Example Question #242 : Radicals

Simplify:

$\sqrt{\frac{6}{3}}$

Possible Answers:

$\sqrt{3}$

$2\sqrt{2}$

$\sqrt{2}$

$\sqrt{6}$

Correct answer:

$\sqrt{2}$

Explanation:

When dividing radicals, we simply divide the numbers inside the radical. Therefore:

$\sqrt{\frac{6}{3}}=\sqrt{2}$

The number inside the radical is a prime number and cannot be simplified any further.

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Algebra II : Radicals

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #142 : Simplifying Radicals

Example Question #241 : Radicals

Example Question #42 : Multiplying And Dividing Radicals

Example Question #151 : Simplifying Radicals

Example Question #4142 : Algebra Ii

Example Question #241 : Radicals

Example Question #242 : Radicals

Example Question #51 : Multiplying And Dividing Radicals

Example Question #52 : Multiplying And Dividing Radicals

Example Question #242 : Radicals

All Algebra II Resources

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