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Algebra II : Simplifying Radicals

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Example Questions

Example Question #151 : Simplifying Radicals

Simplify:

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

Possible Answers:

$4\sqrt{2}$

$2\sqrt{6}$

$4\sqrt{3}$

$4\sqrt{6}$

$2\sqrt{3}$

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 #152 : Simplifying 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 #153 : Simplifying Radicals

Simplify:

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

Possible Answers:

$2\sqrt{3}$

$5\sqrt{7}$

$7\sqrt{5}$

$\sqrt{35}$

$\sqrt{57}$

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:

$6\sqrt{10}$

$\sqrt{80}$

$5\sqrt{6}$

$4\sqrt{5}$

$16\sqrt{5}$

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 #154 : Simplifying Radicals

Simplify:

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

Possible Answers:

$\sqrt{2}$

$\sqrt{3}$

$\sqrt{6}$

$2\sqrt{2}$

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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Example Question #1486 : Mathematical Relationships And Basic Graphs

Simplify:

$\sqrt{\frac{96}{12}}$

Possible Answers:

$2\sqrt{2}$

$\sqrt{6}$

$2\sqrt{3}$

$2\sqrt{6}$

$\sqrt{8}$

Correct answer:

$2\sqrt{2}$

Explanation:

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

$\sqrt{\frac{96}{12}}=\sqrt{8}$

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

$\sqrt{8}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$

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Example Question #54 : Multiplying And Dividing Radicals

Simplify:

$\frac{\sqrt{120}}{\sqrt{24}}$

Possible Answers:

$2\sqrt{5}$

$\sqrt{5}$

$\sqrt{6}$

$\sqrt{7}$

$2\sqrt{2}$

Correct answer:

$\sqrt{5}$

Explanation:

When dividing radicals, we simply divide the numbers inside the radical. Because we are looking for the square root of each number we can place a single radical over the two numbers and solve.

$\frac{\sqrt{120}}{\sqrt{24}}=\sqrt{\frac{120}{24}}=\sqrt{5}$

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

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Example Question #251 : Radicals

Simplify $\frac{\sqrt{45}}{\sqrt{5}}$ .

Possible Answers:

$3\sqrt{5}$

$\sqrt{7}$

It cannot be simplified any further.

Correct answer:

Explanation:

The Quotient Raised to a Power rule states that $\frac{a^{x}}{b^{x}}=(\frac{a}{b})^{x}$ .

Remember that a square root is the equivalent of raising a term to the 1/2 power.

$\frac{a^{1/2}}{b^{1/2}}=\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$

In this case:

$\frac{\sqrt{45}}{\sqrt{5}}=\sqrt{\frac{45}{5}}=\sqrt{9}=3$

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Algebra II : Simplifying Radicals

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #151 : Simplifying Radicals

Example Question #4142 : Algebra Ii

Example Question #152 : Simplifying Radicals

Example Question #153 : Simplifying Radicals

Example Question #51 : Multiplying And Dividing Radicals

Example Question #52 : Multiplying And Dividing Radicals

Example Question #154 : Simplifying Radicals

Example Question #1486 : Mathematical Relationships And Basic Graphs

Example Question #54 : Multiplying And Dividing Radicals

Example Question #251 : Radicals

All Algebra II Resources

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