Chapter 13

Solve for \(x\) and check. $$\sqrt{x}=6$$

Express in radical form. $$a^{1 / 4}$$

Addition and Subtraction of Radicals. Combine as indicated and simplify. $$2 \sqrt{24}-\sqrt{54}$$

Simplify, and write without negative exponents. Do some by calculator. $$3 x^{-1}$$

Solve for \(x\) and check. $$\sqrt{x}+5=9$$

Express in radical form. $$x^{1 / 2}$$

Addition and Subtraction of Radicals. Combine as indicated and simplify. $$\sqrt{300}+\sqrt{108}-\sqrt{243}$$

Simplify, and write without negative exponents. Do some by calculator. $$4 a^{-2}$$

Solve for \(x\) and check. $$\sqrt{7 x+8}=6$$

Express in radical form. $$z^{3 / 4}$$

Addition and Subtraction of Radicals. Combine as indicated and simplify. $$\sqrt{24}-\sqrt{96}+\sqrt{54}$$

Simplify, and write without negative exponents. Do some by calculator. $$2 p^{0}$$

Solve for \(x\) and check. $$\sqrt{3 x-2}=5$$

Express in radical form. $$a^{1 / 2} b^{1 / 4}$$

Addition and Subtraction of Radicals. Combine as indicated and simplify. $$\sqrt{128}-\sqrt{18}+\sqrt{32}$$

Simplify, and write without negative exponents. Do some by calculator. $$(3 m)^{-1}$$

Solve for \(x\) and check. $$\sqrt{2.95 x-1.84}=6.23$$

Express in radical form. $$(m-n)^{1 / 2}$$

Addition and Subtraction of Radicals. Combine as indicated and simplify. $$2 \sqrt{50}+\sqrt{72}+3 \sqrt{18}$$

Simplify, and write without negative exponents. Do some by calculator. $$a(2 b)^{-2}$$

Solve for \(x\) and check. $$\sqrt{5.88 x+4.92}=7.72$$

Express in radical form. $$\left(x^{2} y\right)^{-1 / 2}$$

Addition and Subtraction of Radicals. Combine as indicated and simplify. $$\sqrt[3]{384}-\sqrt[3]{162}+\sqrt[3]{750}$$

Simplify, and write without negative exponents. Do some by calculator. $$x^{2} y^{-1}$$

Solve for \(x\) and check. $$\sqrt{x+1}=\sqrt{2 x-7}$$

Express in radical form. $$\left(\frac{x}{y}\right)^{-1 / 3}$$

Simplify, and write without negative exponents. Do some by calculator. $$a^{3} b^{-2}$$

Solve for \(x\) and check. $$2=\sqrt[4]{1+3 x}$$

Express in radical form. $$a^{0} b^{-3 / 4}$$

Addition and Subtraction of Radicals. Combine as indicated and simplify. $$3 \sqrt[3]{108}+2 \sqrt[3]{32}-\sqrt[3]{256}$$

Simplify, and write without negative exponents. Do some by calculator. $$m^{2} n^{-3}$$

Solve for \(x\) and check. $$\sqrt{3 x+1}=5$$

Addition and Subtraction of Radicals. Combine as indicated and simplify. $$\sqrt[3]{625}-2 \sqrt[3]{135}-\sqrt[3]{320}$$

Simplify, and write without negative exponents. Do some by calculator. $$p^{3} q^{-1}$$

Solve for \(x\) and check. $$\sqrt[3]{2 x}=4$$

Express in exponential form. $$\sqrt[3]{x}$$

Addition and Subtraction of Radicals. Combine as indicated and simplify. $$5 \sqrt[3]{320}+2 \sqrt[3]{40}-4 \sqrt[3]{135}$$

Simplify, and write without negative exponents. Do some by calculator. $$\left(2 x^{2} y^{3} z^{4}\right)^{-1}$$

Solve for \(x\) and check. $$\sqrt{x-3}=\frac{4}{\sqrt{x-3}}$$

Express in exponential form. $$\sqrt{y^{2}}$$

Addition and Subtraction of Radicals. Combine as indicated and simplify. $$\sqrt[4]{768}-\sqrt[4]{48}-\sqrt[4]{243}$$

Simplify, and write without negative exponents. Do some by calculator. $$\left(3 m^{3} n^{2} p\right)^{0}$$

Solve for \(x\) and check. $$x+2=\sqrt{x^{2}+6}$$

Express in exponential form. $$4 \sqrt[3]{x y}$$

Addition and Subtraction of Radicals. Combine as indicated and simplify. $$3 \sqrt{\frac{5}{4}}+2 \sqrt{45}$$

Simplify, and write without negative exponents. Do some by calculator. $$\left(5 p^{2} q^{2} r^{2}\right)^{3}$$

Solve for \(x\) and check. $$\sqrt{x^{2}-7.25}=8.75-x$$

Addition and Subtraction of Radicals. Combine as indicated and simplify. $$\sqrt{128 x^{2} y}-\sqrt{98 x^{2} y}+\sqrt{162 x^{2} y}$$

Simplify, and write without negative exponents. Do some by calculator. $$\left(4 a^{3} b^{2} c^{6}\right)^{-2}$$

Express in exponential form. $$\sqrt[n]{x^{m}}$$