Q. 8.48 Simplify:a聽48m7n2100m5n8聽聽b聽... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.48 (page 769)

Simplify:
$(a) \sqrt{\frac{48 m^{7} n^{2}}{100 m^{5} n^{8}}} (b) \sqrt[3]{\frac{54 x^{7} y^{5}}{250 x^{2} y^{2}}} (c) \sqrt[4]{\frac{32 a^{9} b^{7}}{162 a^{3} b^{3}}} .$

Short Answer

Expert verified

Part a. After simplifying we get, $\frac{2 m \sqrt{3}}{5 n^{3}} .$

Part b. After simplifying we get, $\frac{3 x y \sqrt[3]{x^{2}}}{5} .$

Part c. After simplifying we get, $\frac{2 a b \sqrt[4]{a^{2}}}{3} .$

Step by step solution

Part a Step 1. Simplify the fraction in the radicand

Given: $\sqrt{\frac{48 m^{7} n^{2}}{100 m^{5} n^{8}}}$

After simplifying the fraction in the radicand we get,

$\sqrt{\frac{48 m^{7 - 5} n^{2 - 8}}{100}} = \sqrt{\frac{12 m^{2} n^{- 6}}{25}} = \sqrt{\frac{12 m^{2}}{25 n^{6}}}$

Part a Step 2. Use the Quotient property to rewrite the radical as the quotient of two radicals

So, we get $\frac{\sqrt{12 m^{2}}}{\sqrt{25 n^{6}}} .$

Part a Step 3. Simplify the radicals of both the numerator and denominator

After simplifying we get,

$\frac{\sqrt{12 m^{2}}}{\sqrt{25 n^{6}}} = \frac{\sqrt{{(2 m)}^{2}} 路 \sqrt{3}}{\sqrt{{(5 n^{3})}^{2}}} = \frac{2 m \sqrt{3}}{5 n^{3}}$

Part b Step 1. Simplify the fraction in the radicand

Given: $\sqrt[3]{\frac{54 x^{7} y^{5}}{250 x^{2} y^{2}}}$

After simplifying the fraction in the radicand we get,

$\sqrt[3]{\frac{27 x^{7 - 2} y^{5 - 2}}{125}} = \sqrt[3]{\frac{27 x^{5} y^{3}}{125}}$

Part b Step 2. Use the Quotient property to rewrite the radical as the quotient of two radicals

So, we get $\frac{\sqrt[3]{27 x^{5} y^{3}}}{\sqrt[3]{125}} .$

Part b Step 3. Simplify the radicals of both the numerator and denominator

After simplifying we get,

$\frac{\sqrt[3]{27 x^{5} y^{3}}}{\sqrt[3]{125}} = \frac{\sqrt[3]{{(3 x y)}^{3}} 路 \sqrt[3]{x^{2}}}{\sqrt[3]{{(5)}^{3}}} = \frac{3 x y \sqrt[3]{x^{2}}}{5}$

Part c Step 1. Simplify the fraction in the radicand

Given: $\sqrt[4]{\frac{32 a^{9} b^{7}}{162 a^{3} b^{3}}}$

After simplifying the fraction in the radicand we get,

$\sqrt[4]{\frac{16 a^{9 - 3} b^{7 - 3}}{81}} = \sqrt[4]{\frac{16 a^{6} b^{5}}{81}}$

Part c Step 2. Use the Quotient property to rewrite the radical as the quotient of two radicals

So, we get $\frac{\sqrt[4]{16 a^{6} b^{4}}}{\sqrt[4]{81}} .$

Part c Step 3. Simplify the radicals of both the numerator and denominator

After simplifying we get,

$\frac{\sqrt[4]{16 a^{6} b^{4}}}{\sqrt[4]{81}} = \frac{\sqrt[4]{{(2 a b)}^{4}} 路 \sqrt[4]{a^{2}}}{\sqrt[4]{{(3)}^{4}}} = \frac{2 a b \sqrt[4]{a^{2}}}{3}$

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91影视

Simplify:
$(a) \sqrt{\frac{48 m^{7} n^{2}}{100 m^{5} n^{8}}} (b) \sqrt[3]{\frac{54 x^{7} y^{5}}{250 x^{2} y^{2}}} (c) \sqrt[4]{\frac{32 a^{9} b^{7}}{162 a^{3} b^{3}}} .$

Short Answer

Step by step solution

Part a Step 1. Simplify the fraction in the radicand

Part a Step 2. Use the Quotient property to rewrite the radical as the quotient of two radicals

Part a Step 3. Simplify the radicals of both the numerator and denominator

Part b Step 1. Simplify the fraction in the radicand

Part b Step 2. Use the Quotient property to rewrite the radical as the quotient of two radicals

Part b Step 3. Simplify the radicals of both the numerator and denominator

Part c Step 1. Simplify the fraction in the radicand

Part c Step 2. Use the Quotient property to rewrite the radical as the quotient of two radicals

Part c Step 3. Simplify the radicals of both the numerator and denominator

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91影视

Simplify:a48m7n2100m5n8b54x7y5250x2y23c32a9b7162a3b34.

Short Answer

Step by step solution

Part a Step 1. Simplify the fraction in the radicand

Part a Step 2. Use the Quotient property to rewrite the radical as the quotient of two radicals

Part a Step 3. Simplify the radicals of both the numerator and denominator

Part b Step 1. Simplify the fraction in the radicand

Part b Step 2. Use the Quotient property to rewrite the radical as the quotient of two radicals

Part b Step 3. Simplify the radicals of both the numerator and denominator

Part c Step 1. Simplify the fraction in the radicand

Part c Step 2. Use the Quotient property to rewrite the radical as the quotient of two radicals

Part c Step 3. Simplify the radicals of both the numerator and denominator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

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Mechanics Maths

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Simplify:
$(a) \sqrt{\frac{48 m^{7} n^{2}}{100 m^{5} n^{8}}} (b) \sqrt[3]{\frac{54 x^{7} y^{5}}{250 x^{2} y^{2}}} (c) \sqrt[4]{\frac{32 a^{9} b^{7}}{162 a^{3} b^{3}}} .$