Exam 8: Roots, Radicals, and Root Functions

Solve the problem. Give the answer as a simplified radical expression. -Find the perimeter of a lot with sides measuring $5 \sqrt{50}, 2 \sqrt{18}, 3 \sqrt{8}$ , and $2 \sqrt{12}$ yards.

(Multiple Choice)

4.9/5

(31)

Question 141

Write with radicals. Assume that all variables represent positive real numbers - $\left(x^{8} y^{8}\right)^{1 / 3}$

(Multiple Choice)

4.9/5

(31)

Question 142

Graph the function and give its domain and its range. - $f(x)=\sqrt{x-5}$ $Graph the function and give its domain and its range. - f(x)=\sqrt{x-5}$

(Multiple Choice)

4.9/5

(34)

Question 143

Simplify the radical. Assume that all variables represent positive real numbers. - $\sqrt[4]{48^{2}}$

(Multiple Choice)

4.8/5

(35)

Question 144

$\mathrm{i}^{3}=-\mathrm{i}$

(True/False)

4.7/5

(40)

Question 145

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[3]{8 k^{6}}$

(Multiple Choice)

4.8/5

(35)

Question 146

Find the equation of a circle satisfying the given conditions. -Center: $(4,0)$ ; radius: $\sqrt{5}$

(Multiple Choice)

4.9/5

(33)

Question 147

Write the expression in lowest terms. Assume that all variables represent positive real numbers. - $\frac{12+18 \sqrt{128}}{18}$

(Multiple Choice)

4.9/5

(40)

Question 148

Simplify the expression involving rational exponents. - $512^{1 / 3}$

(Multiple Choice)

4.8/5

(29)

Question 149

Rationalize the denominator. Assume that all variables represent positive real numbers. - $-\sqrt{\frac{245 \mathrm{x}^{3}}{\mathrm{y} 5}}$

(Multiple Choice)

4.8/5

(35)

Question 150

Graph the function and give its domain and its range. - $f(x)=\sqrt{x+2}$ $Graph the function and give its domain and its range. - f(x)=\sqrt{x+2}$

(Multiple Choice)

4.9/5

(28)

Question 151

Simplify. Assume that all variables represent positive real numbers. - $(5-2 \sqrt{5})^{2}$

(Multiple Choice)

4.7/5

(35)

Question 152

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\sqrt[7]{\mathrm{x}} \cdot \sqrt{\mathrm{x}}$

(Multiple Choice)

4.9/5

(44)

Question 153

Write the number as a product of a real number and $i$ . Simplify the radical expression. - $\sqrt{-124}$

(Multiple Choice)

4.7/5

(40)

Question 154

Simplify. Assume that all variables represent positive real numbers. - $\sqrt[4]{\frac{6}{7}}$

(Multiple Choice)

4.9/5

(31)

Question 155

Write the expression in the form a + bi. - $\frac{-9 \mathrm{i}}{8-6 \mathrm{i}}$

(Multiple Choice)

4.7/5

(35)

Question 156

Write the number as a product of a real number and $i$ . Simplify the radical expression. - $\sqrt{-245}$

(Multiple Choice)

4.8/5

(37)

Question 157

The following table gives data on two different solar modules being developed for use in roofing. You must determine the size of the frame needed to support each panel on a roof. (Note: The sides of each frame will form a right triangle, and the hypotenuse of the triangle will be the width of the panel.) Use the Pythagorean theorem to find the dimensions of the legs for each frame if one leg is twice the length of the other. Round your answers to the nearest tenth when necessary.

(Multiple Choice)

4.9/5

(39)

Question 158

Write the expression in the form a + bi. - $\frac{8}{4-6 i}$

(Multiple Choice)

4.8/5

(35)

Question 159

Rationalize the denominator. Assume that all variables represent positive real numbers. - $\frac{9 a}{\sqrt{5}}$

(Multiple Choice)

4.8/5

(35)

Question 160

Showing 141 - 160 of 358

Solve the problem. Give the answer as a simplified radical expression. -Find the perimeter of a lot with sides measuring $5 \sqrt{50}, 2 \sqrt{18}, 3 \sqrt{8}$ , and $2 \sqrt{12}$ yards.

Write with radicals. Assume that all variables represent positive real numbers - $\left(x^{8} y^{8}\right)^{1 / 3}$

Graph the function and give its domain and its range. - $f(x)=\sqrt{x-5}$ $Graph the function and give its domain and its range. - f(x)=\sqrt{x-5}$

Simplify the radical. Assume that all variables represent positive real numbers. - $\sqrt[4]{48^{2}}$

$\mathrm{i}^{3}=-\mathrm{i}$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[3]{8 k^{6}}$

Find the equation of a circle satisfying the given conditions. -Center: $(4,0)$ ; radius: $\sqrt{5}$

Write the expression in lowest terms. Assume that all variables represent positive real numbers. - $\frac{12+18 \sqrt{128}}{18}$

Simplify the expression involving rational exponents. - $512^{1 / 3}$

Rationalize the denominator. Assume that all variables represent positive real numbers. - $-\sqrt{\frac{245 \mathrm{x}^{3}}{\mathrm{y} 5}}$

Graph the function and give its domain and its range. - $f(x)=\sqrt{x+2}$ $Graph the function and give its domain and its range. - f(x)=\sqrt{x+2}$

Simplify. Assume that all variables represent positive real numbers. - $(5-2 \sqrt{5})^{2}$

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\sqrt[7]{\mathrm{x}} \cdot \sqrt{\mathrm{x}}$

Write the number as a product of a real number and $i$ . Simplify the radical expression. - $\sqrt{-124}$

Simplify. Assume that all variables represent positive real numbers. - $\sqrt[4]{\frac{6}{7}}$

Write the expression in the form a + bi. - $\frac{-9 \mathrm{i}}{8-6 \mathrm{i}}$

Write the number as a product of a real number and $i$ . Simplify the radical expression. - $\sqrt{-245}$

Write the expression in the form a + bi. - $\frac{8}{4-6 i}$

Rationalize the denominator. Assume that all variables represent positive real numbers. - $\frac{9 a}{\sqrt{5}}$

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

Solve the problem. Give the answer as a simplified radical expression. -Find the perimeter of a lot with sides measuring 550,218,385 \sqrt{50}, 2 \sqrt{18}, 3 \sqrt{8}550​,218​,38​ , and 2122 \sqrt{12}212​ yards.

Write with radicals. Assume that all variables represent positive real numbers - (x8y8)1/3\left(x^{8} y^{8}\right)^{1 / 3}(x8y8)1/3

Graph the function and give its domain and its range. - f(x)=x−5f(x)=\sqrt{x-5}f(x)=x−5​

Simplify the radical. Assume that all variables represent positive real numbers. - 4824\sqrt[4]{48^{2}}4482​

i3=−i\mathrm{i}^{3}=-\mathrm{i}i3=−i

Express the radical in simplified form.Assume that all variables represent positive real numbers. - 8k63\sqrt[3]{8 k^{6}}38k6​

Find the equation of a circle satisfying the given conditions. -Center: (4,0)(4,0)(4,0) ; radius: 5\sqrt{5}5​

Write the expression in lowest terms. Assume that all variables represent positive real numbers. - 12+1812818\frac{12+18 \sqrt{128}}{18}1812+18128​​

Simplify the expression involving rational exponents. - 5121/3512^{1 / 3}5121/3

Rationalize the denominator. Assume that all variables represent positive real numbers. - −245x3y5-\sqrt{\frac{245 \mathrm{x}^{3}}{\mathrm{y} 5}}−y5245x3​​

Graph the function and give its domain and its range. - f(x)=x+2f(x)=\sqrt{x+2}f(x)=x+2​

Simplify. Assume that all variables represent positive real numbers. - (5−25)2(5-2 \sqrt{5})^{2}(5−25​)2

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - x7⋅x\sqrt[7]{\mathrm{x}} \cdot \sqrt{\mathrm{x}}7x​⋅x​

Write the number as a product of a real number and iii . Simplify the radical expression. - −124\sqrt{-124}−124​

Simplify. Assume that all variables represent positive real numbers. - 674\sqrt[4]{\frac{6}{7}}476​​

Write the expression in the form a + bi. - −9i8−6i\frac{-9 \mathrm{i}}{8-6 \mathrm{i}}8−6i−9i​

Write the number as a product of a real number and iii . Simplify the radical expression. - −245\sqrt{-245}−245​

Write the expression in the form a + bi. - 84−6i\frac{8}{4-6 i}4−6i8​

Rationalize the denominator. Assume that all variables represent positive real numbers. - 9a5\frac{9 a}{\sqrt{5}}5​9a​

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

Solve the problem. Give the answer as a simplified radical expression. -Find the perimeter of a lot with sides measuring $5 \sqrt{50}, 2 \sqrt{18}, 3 \sqrt{8}$ , and $2 \sqrt{12}$ yards.

Write with radicals. Assume that all variables represent positive real numbers - $\left(x^{8} y^{8}\right)^{1 / 3}$

Graph the function and give its domain and its range. - $f(x)=\sqrt{x-5}$ $Graph the function and give its domain and its range. - f(x)=\sqrt{x-5}$

Simplify the radical. Assume that all variables represent positive real numbers. - $\sqrt[4]{48^{2}}$

$\mathrm{i}^{3}=-\mathrm{i}$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[3]{8 k^{6}}$

Find the equation of a circle satisfying the given conditions. -Center: $(4,0)$ ; radius: $\sqrt{5}$

Write the expression in lowest terms. Assume that all variables represent positive real numbers. - $\frac{12+18 \sqrt{128}}{18}$

Simplify the expression involving rational exponents. - $512^{1 / 3}$

Rationalize the denominator. Assume that all variables represent positive real numbers. - $-\sqrt{\frac{245 \mathrm{x}^{3}}{\mathrm{y} 5}}$

Graph the function and give its domain and its range. - $f(x)=\sqrt{x+2}$ $Graph the function and give its domain and its range. - f(x)=\sqrt{x+2}$

Simplify. Assume that all variables represent positive real numbers. - $(5-2 \sqrt{5})^{2}$

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\sqrt[7]{\mathrm{x}} \cdot \sqrt{\mathrm{x}}$

Write the number as a product of a real number and $i$ . Simplify the radical expression. - $\sqrt{-124}$

Simplify. Assume that all variables represent positive real numbers. - $\sqrt[4]{\frac{6}{7}}$

Write the expression in the form a + bi. - $\frac{-9 \mathrm{i}}{8-6 \mathrm{i}}$

Write the number as a product of a real number and $i$ . Simplify the radical expression. - $\sqrt{-245}$

Write the expression in the form a + bi. - $\frac{8}{4-6 i}$

Rationalize the denominator. Assume that all variables represent positive real numbers. - $\frac{9 a}{\sqrt{5}}$