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Common Core: High School - Number and Quantity : The Real Number System

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

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All Common Core: High School - Number and Quantity Resources

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Example Questions

Example Question #11 : The Real Number System

Evaluate: $100^{\frac{1}{2}}$

Possible Answers:

200

Correct answer:

Explanation:

To evaluate this, let's rewrite the problem.

$100^{\frac{1}{2}}=\sqrt{100}$

Now lets break down the square root.

$\sqrt{100}=\sqrt{10\cdot10}=\sqrt{10^2}=10$

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Example Question #12 : The Real Number System

Rewrite $84^{\frac{1}{3}}$ , in radical form.

Possible Answers:

$\sqrt[3]{84}$

$\sqrt[84]{3}$

$\sqrt[3]{\frac{84}{3}}$

$84^{\frac{1}{3}}$

Correct answer:

$\sqrt[3]{84}$

Explanation:

To determine what the root is, we look at the denominator of the exponent. In this case the root is , so we will write it in the following way.

$84^{\frac{1}{3}}=\sqrt[3]{84}$

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Example Question #13 : The Real Number System

Rewrite $17^{\frac{1}{5}}$ , in radical form.

Possible Answers:

$17^{\frac{1}{5}}$

$\sqrt[5]{\frac{17}{5}}$

$\sqrt[17]{5}$

$\sqrt[5]{17}$

Correct answer:

$\sqrt[5]{17}$

Explanation:

To determine what the root is, we look at the denominator of the exponent. In this case the root is , so we will write it in the following way.

$17^{\frac{1}{5}}=\sqrt[5]{17}$

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Example Question #14 : The Real Number System

Rewrite $92^{\frac{3}{4}}$ , in radical form.

Possible Answers:

$(\sqrt[4]{92})^3$

$(\sqrt[3]{92})^4$

$\sqrt[3]{\frac{92}{4}}$

$\sqrt[4]{\frac{92}{3}}$

Correct answer:

$(\sqrt[4]{92})^3$

Explanation:

To determine what the root is, we look at the denominator of the exponent. In this case the root is , and the numerator tells us what power we are raising the entire expression to, which is .

$92^{\frac{3}{4}}=(\sqrt[4]{92})^3$

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Example Question #15 : The Real Number System

Rewrite $59^{\frac{3}{8}}$ , in radical form.

Possible Answers:

$(\sqrt[3]{59})^8$

$\sqrt[8]{\frac{59}{3}}$

$\sqrt[3]{\frac{59}{8}}$

$(\sqrt[8]{59})^3$

Correct answer:

$(\sqrt[8]{59})^3$

Explanation:

To determine what the root is, we look at the denominator of the exponent. In this case the root is , and the numerator tells us what power we are raising the entire expression to, which is .

$59^{\frac{3}{8}}=(\sqrt[8]{59})^3$

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Example Question #16 : The Real Number System

Rewrite $56^{\frac{5}{4}}$ , in radical form.

Possible Answers:

$(\sqrt[4]{56})^5$

$\sqrt[5]{\frac{56}{4}}$

$\sqrt[4]{\frac{56}{5}}$

$(\sqrt[5]{56})^4$

Correct answer:

$(\sqrt[4]{56})^5$

Explanation:

To determine what the root is, we look at the denominator of the exponent. In this case the root is , and the numerator tells us what power we are raising the entire expression to, which is .

$56^{\frac{5}{4}}=(\sqrt[4]{56})^5$

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Example Question #17 : The Real Number System

Rewrite $116^{\frac{1}{5}}$ , in radical form.

Possible Answers:

$\sqrt[116]{5}$

$\sqrt[5]{116}$

$116^{\frac{1}{5}}$

$\sqrt[5]{\frac{116}{5}}$

Correct answer:

$\sqrt[5]{116}$

Explanation:

To determine what the root is, we look at the denominator of the exponent. In this case the root is , so we will write it in the following way.

$116^{\frac{1}{5}}=\sqrt[5]{116}$

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Example Question #18 : The Real Number System

Rewrite $86^{\frac{1}{6}}$ , in radical form.

Possible Answers:

$86^{\frac{1}{6}}$

$\sqrt[6]{\frac{86}{6}}$

$\sqrt[6]{86}$

$\sqrt[86]{6}$

Correct answer:

$\sqrt[6]{86}$

Explanation:

To determine what the root is, we look at the denominator of the exponent. In this case the root is , so we will write it in the following way.

$86^{\frac{1}{6}}=\sqrt[6]{86}$

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Example Question #19 : The Real Number System

Rewrite $111^{\frac{5}{6}}$ , in radical form.

Possible Answers:

$\sqrt[5]{\frac{111}{6}}$

$(\sqrt[5]{111})^6$

$(\sqrt[6]{111})^5$

$\sqrt[6]{\frac{111}{5}}$

Correct answer:

$(\sqrt[6]{111})^5$

Explanation:

To determine what the root is, we look at the denominator of the exponent. In this case the root is , and the numerator tells us what power we are raising the entire expression to, which is .

$111^{\frac{5}{6}}=(\sqrt[6]{111})^5$

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Example Question #20 : The Real Number System

Rewrite $58^{\frac{2}{7}}$ , in radical form.

Possible Answers:

$\sqrt[]{\frac{58}{7}}$

$(\sqrt[]{58})^7$

$\sqrt[7]{\frac{58}{2}}$

$(\sqrt[7]{58})^2$

Correct answer:

$(\sqrt[7]{58})^2$

Explanation:

To determine what the root is, we look at the denominator of the exponent. In this case the root is , and the numerator tells us what power we are raising the entire expression to, which is .

$58^{\frac{2}{7}}=(\sqrt[7]{58})^2$

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All Common Core: High School - Number and Quantity Resources

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Common Core: High School - Number and Quantity : The Real Number System

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #11 : The Real Number System

Example Question #12 : The Real Number System

Example Question #13 : The Real Number System

Example Question #14 : The Real Number System

Example Question #15 : The Real Number System

Example Question #16 : The Real Number System

Example Question #17 : The Real Number System

Example Question #18 : The Real Number System

Example Question #19 : The Real Number System

Example Question #20 : The Real Number System

All Common Core: High School - Number and Quantity Resources

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