Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 6 - Polygons and Quadrilaterals - Algebra Review - Page 399: 15


${\frac{3 \sqrt {10}}{2}}$

Work Step by Step

First, we write both numbers in the numerator under the same radical: $\frac{\sqrt {3} • \sqrt {15}}{\sqrt {2}} = \sqrt {\frac{3 • 15}{2}}$ Multiply what is under the radical sign first: $\sqrt {\frac{45}{2}}$ Rationalize the fraction by multiplying both the numerator and denominator by $\sqrt 2$: $\sqrt {\frac{45}{2}} • \frac{\sqrt 2}{\sqrt 2}$ Multiply to simplify: ${\frac{\sqrt {45} • \sqrt 2}{2}}$ Multiply the terms in the numerator: ${\frac{\sqrt {90}}{2}}$ Rewrite $90$ as the product of a perfect square and another number: ${\frac{\sqrt {9 • 10}}{2}}$ Take the square root of $9$ to move it out from under the square root sign: ${\frac{3 \sqrt {10}}{2}}$
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