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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 300 (page 824)

In the following exercises, solve.
$\sqrt{5 v - 2} + 5 = 0$

Short Answer

Expert verified

The given equation has no solution.

Step by step solution

01

Step 1. Given information.

The given equation is:

$\sqrt{5 v - 2} + 5 = 0$

02

Step 2. Solve the equation.

The given equation can be written as:

$\sqrt{5 v - 2} = - 5$

For all real value of $x, \sqrt{x} \geq 0$ .

In other words, a radical value cannot be equal to a negative value.

So, $\sqrt{5 v - 2} \neq - 5$ for any real value of $v$ .

03

Step 3. Conclusion.

The given equation has no solution.

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{50 r^{5} s^{2}}{128 r^{2} s^{6}}}$

(b) $\sqrt[3]{\frac{24 m^{9} n^{7}}{375 m^{4} n}}$

(c) $\sqrt[4]{\frac{81 m^{2} n^{8}}{256 m n^{2}}}$

In the following exercises, solve.

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

In the following exercises, simplify using absolute value signs as needed. $\sqrt{147 m^{7} n^{11}}, \sqrt[3]{48 x^{6} y^{7}}, \sqrt[4]{32 x^{5} y^{4}}$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{75 r^{9}}{s^{8}}}$

(b) $\sqrt[3]{\frac{54 a^{8}}{b^{3}}}$

(c) $\sqrt[4]{\frac{64 c^{5}}{d^{4}}}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{96 r^{3} s^{3}}, \sqrt[3]{80 x^{7} y^{6}}, \sqrt[4]{80 x^{8} y^{9}}$

See all solutions

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