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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 519. (page 1125)

Simplify: $\sqrt[4]{486 u^{7}} + \sqrt[4]{768 u^{3}}$

Short Answer

Expert verified

$\sqrt[4]{486 u^{7}} + \sqrt[4]{768 u^{3}} = 3 u \sqrt[4]{6 u^{3}} + 4 \sqrt[4]{3 u^{3}}$

Step by step solution

01

Given Information

Given Expression is $\sqrt[4]{486 u^{7}} + \sqrt[4]{768 u^{3}}$ .

02

Simplification

$\sqrt[4]{486 u^{7}} + \sqrt[4]{768 u^{3}}$

Rewrite each radicand using perfect fourth power factors

role="math" localid="1650386923400" $= \sqrt[4]{81 u^{4} . 6 u^{3}} + \sqrt[4]{4^{4} . 3 u^{3}}$

Rewrite the perfect fourth powers

role="math" localid="1650386973788" $= \sqrt[4]{{(3 u)}^{4} . 6 u^{3}} + \sqrt[4]{{(4)}^{4} . 3 u^{3}}$

Simplify

$= 3 u \sqrt[4]{6 u^{3}} + 4 \sqrt[4]{3 u^{3}}$

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