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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 291 (page 824)

In the following exercises, solve.
$\sqrt[3]{2 x} = - 2$

Short Answer

Expert verified

The solution of the given equation is $x = - 4$ .

Step by step solution

01

Step 1. Given information.

The given equation is:

$\sqrt[3]{2 x} = - 2$

02

Step 2. Solve the equation.

Take cube on both sides.

$\begin{array}{rcl} (\sqrt[3]{2 x})^{3} & = & (- 2)^{3} \\ 2 x & = & - 8 \\ \frac{2 x}{2} & = & \frac{- 8}{2} \\ x & = & - 4 \end{array}$

03

Step 3. Conclusion.

The solution of the given equation is $x = - 4$ .

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Most popular questions from this chapter

In the following exercises, solve.
$\sqrt{6 n + 1} + 4 = 8$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{32 x^{5} y^{3}}{18 x^{3} y}}$

(b) $\sqrt[3]{\frac{5 x^{6} y^{9}}{40 x^{5} y^{3}}}$

(c) $\sqrt[4]{\frac{5 a^{8} b^{6}}{80 a^{3} b^{2}}}$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{45 r^{3}}{s^{10}}}$

(b) $\sqrt[3]{\frac{625 u^{10}}{v^{3}}}$

(c) $\sqrt[4]{\frac{729 c^{21}}{d^{8}}}$

In the following exercise, write as a radical expression.

ⓐ x^{\frac{1}{2}} ⓑ y^{\frac{1}{3}} ⓒ z^{\frac{1}{4}}

Write with a rational exponent:

(a) $\sqrt[7]{3 k}$

(b) $\sqrt[4]{5 j}$

(c) $8 \sqrt[3]{2 a}$

See all solutions

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