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Elementary Algebra

Found in: Page 1077

Book edition 2nd

Author(s) Lynn Marecek, MaryAnne Anthony-Smith

Pages 1240 pages

ISBN 9780998625713

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Short Answer

In the following exercises, simplify.
$(\sqrt{35 y^{3}}) (\sqrt{7 y^{3}})$

The simplified form of the given expression is $7 \sqrt{5} y^{3}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given expression is:

$(\sqrt{35 y^{3}}) (\sqrt{7 y^{3}})$

Step 2. Determine the simplified form.

The given expression can be written as:

$\begin{array}{rcl} (\sqrt{35 y^{3}}) (\sqrt{7 y^{3}}) & = & \sqrt{(35 \cdot 7) \cdot (y^{3} \cdot y^{3})} \\ = & \sqrt{(245) \cdot (y^{6})} \\ = & \sqrt{49} \cdot \sqrt{5} \cdot \sqrt{y^{6}} \\ = & 7 \cdot \sqrt{5} \cdot y^{3} \\ = & 7 \sqrt{5} y^{3} \end{array}$

Step 3. Conclusion.

The simplified form of the given expression is $7 \sqrt{5} y^{3}$ .

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Accident investigation: An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 117 feet. Use the formula $s = \sqrt{24 d}$ to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.

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