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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 22 (page 755)

In the following exercises, estimate each root between two consecutive whole numbers.
鈸� $\sqrt{172}$ 鈸� $\sqrt[3]{200}$

Short Answer

Expert verified

Part (a)

Part (b)

Step by step solution

01

Part (a) Step 1. Given information

(a) $\sqrt{172}$

Estimate each root between two consecutive whole numbers.

02

Step 2. Explanaiton

Think of the perfect square numbers closest to $172$ .

Make a small table of these perfect squares and their squares roots.

\begin{matrix} Numbr & Squareroot \\ \begin{array}{l} 169 \\ 196 \end{array} & \begin{array}{l} 13 \\ 14 \end{array} \end{matrix}

Loca between two consecutive perfect squares.

$169 < 172 < 196$

$\sqrt{172}$ is between their square roots.

03

Psrt (b) Step 3. Given information

(b) $\sqrt[3]{200}$

Estimate each root between two consecutive whole numbers.

04

Step 4. Explanation

Similarly, we locate $200$ between two perfect cube numbers.

$\begin{matrix} Number & Cuberoot \\ \begin{array}{l} 125 \\ 216 \end{array} & \begin{array}{l} 5 \\ 6 \end{array} \end{matrix}$

Locate $200$ between two consecutive perfect cubes.

$鈬� 125 < 200 < 216$

$\sqrt[3]{200}$ is between their cube roots.

$5 < \sqrt[3]{200} < 6$

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{75 r^{6} s^{8}}{48 r s^{4}}}$

(b) $\sqrt[3]{\frac{24 x^{8} y 4}{81 x^{2} y}}$

(c) $\sqrt[4]{\frac{32 m^{9} n^{2}}{162 m n^{2}}}$

In the following exercises, use the Product Property to simplify radical expression $\sqrt{125} .$

In the following exercises, write with a rational exponent.

$鈸� \sqrt[8]{r} 鈸� \sqrt[10]{s} 鈸� \sqrt[4]{t}$

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

Simplify:

a. ${(81 n^{\frac{2}{5}})}^{\frac{3}{2}}$ b. ${(a^{\frac{3}{2}} b^{\frac{1}{2}})}^{\frac{4}{3}}$

See all solutions

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