Chapter 7

Simplify. $$ 6 \sqrt{18}+3 \sqrt{50} $$

Multiply, if possible. Then simplify. $$ \sqrt[3]{9} \cdot \sqrt[3]{-24} $$

Simplify each expression. $$2^{\frac{1}{2}} \cdot 32^{\frac{1}{2}}$$

Find all the real cube roots of each number. $$ -\frac{27}{216} $$

Graph each function. \(y=\sqrt{x-4}\)

Find the inverse of each function. Is the inverse a function? $$ y=5-2 x^{2} $$

Solve. \((x-2)^{\frac{2}{3}}=9\)

Let \(f(x)=3 x+5\) and \(g(x)=x^{2} .\) Perform each function operation. $$ (f-g)(x) $$

Simplify. $$ 14 \sqrt{20}-3 \sqrt{125} $$

Multiply, if possible. Then simplify. $$ \sqrt[3]{-12} \cdot \sqrt[3]{-18} $$

Simplify each expression. $$3^{\frac{1}{3}} \cdot 9^{\frac{1}{3}}$$

Find all the real cube roots of each number. $$ 0.000343 $$

Graph each function. \(y=3 \sqrt{x}\)

Solve. \(3(x-2)^{\frac{3}{4}}=24\)

Let \(f(x)=3 x+5\) and \(g(x)=x^{2} .\) Perform each function operation. $$ (g-f)(x) $$

Simplify. $$ \sqrt{18}+\sqrt{32} $$

Simplify. Assume that all variables are positive. $$ \sqrt{20 x^{3}} $$

Simplify each expression. $$ 3^{\frac{1}{4}} \cdot 27^{\frac{1}{4}} $$

Find all the real fourth roots of each number. $$ 16 $$

Graph each function. \(y=-0.25 \sqrt{x}\)

Solve. \(3(x+3)^{\frac{3}{4}}=81\)

Let \(f(x)=3 x+5\) and \(g(x)=x^{2} .\) Perform each function operation. $$ (f \cdot g)(x) $$

Simplify. $$ \sqrt[3]{54}+\sqrt[3]{16} $$

Simplify. Assume that all variables are positive. $$ \sqrt[3]{81 x^{2}} $$

Write each expression in radical form. $$ x^{\frac{1}{6}} $$

Graph each function. \(y=\frac{1}{3} \sqrt{x}\)

Find the inverse of each function. Is the inverse a function? $$ y=(x+1)^{2} $$

Solve. \((x+1)^{\frac{3}{2}}-2=25\)

Let \(f(x)=3 x+5\) and \(g(x)=x^{2} .\) Perform each function operation. $$ \left(\frac{f}{g}\right)(x) $$

Simplify. $$ 3 \sqrt[3]{81}-2 \sqrt[3]{54} $$

Simplify. Assume that all variables are positive. $$ \sqrt{50 x^{5}} $$

Write each expression in radical form. $$ x^{\frac{1}{5}} $$

Find all the real fourth roots of each number. $$ 0.0081 $$

Graph each function. \(y=-\sqrt{x-1}\)

Find the inverse of each function. Is the inverse a function? $$ y=(2-x)^{2} $$

Solve. \(3+(4-x)^{\frac{3}{2}}=11\)

Let \(f(x)=3 x+5\) and \(g(x)=x^{2} .\) Perform each function operation. $$ \left(\frac{g}{f}\right)(x) $$

Simplify. $$ \sqrt[4]{32}+\sqrt[4]{48} $$

Simplify. Assume that all variables are positive. $$ \sqrt[3]{32 a^{5}} $$

Write each expression in radical form. $$ x^{\frac{2}{7}} $$

Find all the real fourth roots of each number. $$ \frac{10,000}{81} $$

Graph each function. \(y=-5 \sqrt{x+2}\)

A spherical water tank holds \(15,000 \mathrm{ft}^{3}\) of water. Find the diameter of the tank. (Hint: \(V=\frac{\pi}{6} d^{3}\))

Find the inverse of each function. Is the inverse a function? $$ y=(1-2 x)^{2}+5 $$

Let \(f(x)=2 x^{2}+x-3\) and \(g(x)=x-1 .\) Perform each function operation and then find the domain. $$ f(x)+g(x) $$

Multiply. $$ (3+\sqrt{5})(1+\sqrt{5}) $$

Simplify. Assume that all variables are positive. $$ \sqrt[3]{54 y^{10}} $$

Write each expression in radical form. $$ y^{\frac{2}{3}} $$

Find each real-number root. $$ \sqrt{36} $$

Graph each function. \(y=-0.75 \sqrt{x}+3\)