Exam 8: Roots, Radicals, and Root Functions

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $\left(16 h^{4} k^{6}\right)^{3 / 2}$

(Multiple Choice)

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Question 341

$X_{L} is I=\frac{E}{R+\left(X_{L}-X_{C}\right)} . . Use this law to solve the problem. -Find \mathrm{I} if E=5+4 i, R=9, X_{L}=7 , and X_{C}=3 .$ $X_{L}$ is $I=\frac{E}{R+\left(X_{L}-X_{C}\right)}$ . . Use this law to solve the problem. -Find $\mathrm{I}$ if $E=5+4 i, R=9, X_{L}=7$ , and $X_{C}=3$ .

(Multiple Choice)

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Question 342

Simplify the root. - $\sqrt[5]{(-8)^{5}}$

(Multiple Choice)

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Question 343

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{\mathrm{p}^{2}-2 \mathrm{p}+73}=\mathrm{p}+5$

(Multiple Choice)

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Question 344

Find the decimal approximation for the radical. Round the answer to three decimal places. - $\sqrt{1.09}$

(Multiple Choice)

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Question 345

Simplify the expression. Assume that all variables represent positive real numbers. - $12^{5 / 8} \cdot 12^{-1 / 8}$

(Multiple Choice)

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Question 346

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt{0.0081}$

(Multiple Choice)

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Question 347

Perform the indicated operation. Give answer in standard form. - $(-3+4 \mathrm{i})-(6+5 \mathrm{i})-14 \mathrm{i}$

(Multiple Choice)

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Question 348

Simplify the expression. Assume that all variables represent positive real numbers. - $\sqrt[3]{x^{2}} \cdot \sqrt[3]{x^{12}}$

(Multiple Choice)

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Question 349

Write the expression in the form a + bi. - $\frac{9+\mathrm{i}}{-6-2 \mathrm{i}}$

(Multiple Choice)

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Question 350

Solve the problem. Give the answer as a simplified radical expression. -A rectangular coal bin has a length of $\sqrt{27}$ feet and a width of $\sqrt{75}$ feet. What is its perimeter?

(Multiple Choice)

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Question 351

Explain why the sum $\sqrt[3]{125}-\sqrt[4]{625}-\sqrt{9}$ can be simplified quickly.

(Essay)

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Question 352

Add or subtract as indicated. Write your answer in the form $a+b i$ . - $(4+10 \mathrm{i})-(10+5 \mathrm{i})+(8+7 \mathrm{i})$

(Multiple Choice)

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Question 353

Find the distance between the points. - $362)(-8,16)$ and $(4,7)$

(Multiple Choice)

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Question 354

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $5 \sqrt{6}-7 \sqrt{24}$

(Multiple Choice)

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Question 355

Provide an appropriate response. -If $a>0$ and $b>0$ , then $\sqrt{-a} \cdot \sqrt{b}=i \sqrt{a b}$ .

(True/False)

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Question 356

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $\sqrt{49}-\sqrt{196}$

(Multiple Choice)

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Question 357

Use a calculator to approximate the root to the nearest thousandth. - $\sqrt[3]{-89}$

(Multiple Choice)

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Question 358

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $\left(16 h^{4} k^{6}\right)^{3 / 2}$

Simplify the root. - $\sqrt[5]{(-8)^{5}}$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{\mathrm{p}^{2}-2 \mathrm{p}+73}=\mathrm{p}+5$

Find the decimal approximation for the radical. Round the answer to three decimal places. - $\sqrt{1.09}$

Simplify the expression. Assume that all variables represent positive real numbers. - $12^{5 / 8} \cdot 12^{-1 / 8}$

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt{0.0081}$

Perform the indicated operation. Give answer in standard form. - $(-3+4 \mathrm{i})-(6+5 \mathrm{i})-14 \mathrm{i}$

Simplify the expression. Assume that all variables represent positive real numbers. - $\sqrt[3]{x^{2}} \cdot \sqrt[3]{x^{12}}$

Write the expression in the form a + bi. - $\frac{9+\mathrm{i}}{-6-2 \mathrm{i}}$

Solve the problem. Give the answer as a simplified radical expression. -A rectangular coal bin has a length of $\sqrt{27}$ feet and a width of $\sqrt{75}$ feet. What is its perimeter?

Explain why the sum $\sqrt[3]{125}-\sqrt[4]{625}-\sqrt{9}$ can be simplified quickly.

Add or subtract as indicated. Write your answer in the form $a+b i$ . - $(4+10 \mathrm{i})-(10+5 \mathrm{i})+(8+7 \mathrm{i})$

Find the distance between the points. - $362)(-8,16)$ and $(4,7)$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $5 \sqrt{6}-7 \sqrt{24}$

Provide an appropriate response. -If $a>0$ and $b>0$ , then $\sqrt{-a} \cdot \sqrt{b}=i \sqrt{a b}$ .

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $\sqrt{49}-\sqrt{196}$

Use a calculator to approximate the root to the nearest thousandth. - $\sqrt[3]{-89}$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 8: Roots, Radicals, and Root Functions

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - (16h4k6)3/2\left(16 h^{4} k^{6}\right)^{3 / 2}(16h4k6)3/2

XLX_{L}XL​ is I=ER+(XL−XC)I=\frac{E}{R+\left(X_{L}-X_{C}\right)}I=R+(XL​−XC​)E​ . . Use this law to solve the problem. -Find I\mathrm{I}I if E=5+4i,R=9,XL=7E=5+4 i, R=9, X_{L}=7E=5+4i,R=9,XL​=7 , and XC=3X_{C}=3XC​=3 .

Simplify the root. - (−8)55\sqrt[5]{(-8)^{5}}5(−8)5​

Choose the one alternative that best completes the statement or answers the question. Solve the equation - p2−2p+73=p+5\sqrt{\mathrm{p}^{2}-2 \mathrm{p}+73}=\mathrm{p}+5p2−2p+73​=p+5

Find the decimal approximation for the radical. Round the answer to three decimal places. - 1.09\sqrt{1.09}1.09​

Simplify the expression. Assume that all variables represent positive real numbers. - 125/8⋅12−1/812^{5 / 8} \cdot 12^{-1 / 8}125/8⋅12−1/8

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - 0.0081\sqrt{0.0081}0.0081​

Perform the indicated operation. Give answer in standard form. - (−3+4i)−(6+5i)−14i(-3+4 \mathrm{i})-(6+5 \mathrm{i})-14 \mathrm{i}(−3+4i)−(6+5i)−14i

Simplify the expression. Assume that all variables represent positive real numbers. - x23⋅x123\sqrt[3]{x^{2}} \cdot \sqrt[3]{x^{12}}3x2​⋅3x12​

Write the expression in the form a + bi. - 9+i−6−2i\frac{9+\mathrm{i}}{-6-2 \mathrm{i}}−6−2i9+i​

Solve the problem. Give the answer as a simplified radical expression. -A rectangular coal bin has a length of 27\sqrt{27}27​ feet and a width of 75\sqrt{75}75​ feet. What is its perimeter?

Explain why the sum 1253−6254−9\sqrt[3]{125}-\sqrt[4]{625}-\sqrt{9}3125​−4625​−9​ can be simplified quickly.

Add or subtract as indicated. Write your answer in the form a+bia+b ia+bi . - (4+10i)−(10+5i)+(8+7i)(4+10 \mathrm{i})-(10+5 \mathrm{i})+(8+7 \mathrm{i})(4+10i)−(10+5i)+(8+7i)

Find the distance between the points. - 362)(−8,16)362)(-8,16)362)(−8,16) and (4,7)(4,7)(4,7)

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - 56−7245 \sqrt{6}-7 \sqrt{24}56​−724​

Provide an appropriate response. -If a>0a>0a>0 and b>0b>0b>0 , then −a⋅b=iab\sqrt{-a} \cdot \sqrt{b}=i \sqrt{a b}−a​⋅b​=iab​ .

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - 49−196\sqrt{49}-\sqrt{196}49​−196​

Use a calculator to approximate the root to the nearest thousandth. - −893\sqrt[3]{-89}3−89​

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $\left(16 h^{4} k^{6}\right)^{3 / 2}$

Simplify the root. - $\sqrt[5]{(-8)^{5}}$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{\mathrm{p}^{2}-2 \mathrm{p}+73}=\mathrm{p}+5$

Find the decimal approximation for the radical. Round the answer to three decimal places. - $\sqrt{1.09}$

Simplify the expression. Assume that all variables represent positive real numbers. - $12^{5 / 8} \cdot 12^{-1 / 8}$

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt{0.0081}$

Perform the indicated operation. Give answer in standard form. - $(-3+4 \mathrm{i})-(6+5 \mathrm{i})-14 \mathrm{i}$

Simplify the expression. Assume that all variables represent positive real numbers. - $\sqrt[3]{x^{2}} \cdot \sqrt[3]{x^{12}}$

Write the expression in the form a + bi. - $\frac{9+\mathrm{i}}{-6-2 \mathrm{i}}$

Solve the problem. Give the answer as a simplified radical expression. -A rectangular coal bin has a length of $\sqrt{27}$ feet and a width of $\sqrt{75}$ feet. What is its perimeter?

Explain why the sum $\sqrt[3]{125}-\sqrt[4]{625}-\sqrt{9}$ can be simplified quickly.

Add or subtract as indicated. Write your answer in the form $a+b i$ . - $(4+10 \mathrm{i})-(10+5 \mathrm{i})+(8+7 \mathrm{i})$

Find the distance between the points. - $362)(-8,16)$ and $(4,7)$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $5 \sqrt{6}-7 \sqrt{24}$

Provide an appropriate response. -If $a>0$ and $b>0$ , then $\sqrt{-a} \cdot \sqrt{b}=i \sqrt{a b}$ .

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $\sqrt{49}-\sqrt{196}$

Use a calculator to approximate the root to the nearest thousandth. - $\sqrt[3]{-89}$