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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 9: Q. 9.82 (page 1061)

Simplify: $\sqrt{27 p^{3}} - \sqrt{48 p^{3}}$

Short Answer

Expert verified

The solution is $- p \sqrt{3 p} .$

Step by step solution

01

Step 1. Given information

Roots: $\sqrt{27 p^{3}} - \sqrt{48 p^{3}}$

02

Step 2. Calculation

We have,

$\sqrt{27 p^{3}} - \sqrt{48 p^{3}} = \sqrt{9 p^{2}} \cdot \sqrt{3 p} - \sqrt{16 p^{2}} \cdot \sqrt{3 p} = 3 p \sqrt{3 p} - 4 p \sqrt{3 p} = - p \sqrt{3 p}$

Therefore, the solution is $- p \sqrt{3 p} .$

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Explain why an equation of the form $\sqrt{x} + 1 = 0$ has no solution.

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