Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 6 - Radical Functions and Rational Exponents - Mid-Chapter Quiz - Page 389: 24

Answer

$26x \sqrt {2}$

Work Step by Step

The radicals have the same index but different radicands (expression inside the radical sign) so they not similar. Simplify both radicals by factoring each radicand so that at least one of the factors is a square. For the first radical, $32=16(2)=4^2(2)$ so: $2\sqrt{32x^2}=2 \sqrt {(4^2)(2)(x^2)}$ Take out the square root of $4^2$ and $x^2$ to obtain: $=(2)(4)(x)\sqrt {2}\\ =8\sqrt{2}$ For the second radical, $72=36(2)=6^2(2)$ so $3\sqrt{72x^2}=3 \sqrt {(6^2)(2)(x^2)}$ Take out the square root of $6^2$ and $x^2$ to obtain: $=(3)(6)(x)\sqrt {2}$ $=18x \sqrt {2}$ Thus, the given expression is equivalent to: $$8x\sqrt2+18x\sqrt2$$ This time, the radicals have the same index and the same radicand so they are now similar. Perform the operation by adding the coefficients and retaining the radical to obtain: $=(8x+18x)\sqrt {2}\\ =26x\sqrt2$
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