Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 10 - Radical Expressions and Equations - 10-2 Simplifying Radicals - Practice and Problem-Solving Exercises - Page 610: 46


$\frac{ \sqrt 2}{t^{2}}$

Work Step by Step

$\frac{2 \sqrt 4 \sqrt 6}{\sqrt 16 \sqrt 3t^{4}}$ $\frac{2 \times 2 \sqrt 6}{4 \sqrt 3t^{4}}$ We simplify the constants $2 \times 2 \div 4 = 1$ $\frac{\sqrt 6}{\sqrt 3t^{4}}$ To simplify this, we cannot have a radical in the denominator. We multiply $\frac{\sqrt 6}{\sqrt 3t^{4}}$ by $\frac{ \sqrt 3t^{4}}{ \sqrt 3t^{4}}$ $\frac{\sqrt 6}{\sqrt 3t^{4}} \times \frac{ \sqrt 3t^{4}}{ \sqrt 3t^{4}}$ $\frac{ \sqrt 18t^{4}}{ \sqrt (3t^{4})^{2}}$ Square root of $(3t^{4})^{2}$ is $3t^{4}$ because $3t^{4}$ x $3t^{4}$ = $(3t^{4})^{2}$ $\frac{ \sqrt 18t^{4}}{ 3t^{4}}$ The factors of $\sqrt 18t^{4}$ is $\sqrt 9t^{4} \times \sqrt 2$ $\frac{\sqrt 9t^{4} \times \sqrt 2}{ 3t^{4}}$ The square root of $\sqrt 9t^{4}$ is $3t^{2}$ because $3t^{2}$ x $3t^{2}$ = $\sqrt 9t^{4}$ $\frac{ 3t^{2} \sqrt 2}{ 3t^{4}}$ $3t^{2} \div 3t^{4}$ = $t^{2}$ $\frac{ \sqrt 2}{t^{2}}$
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