Chapter 8: Q. 8.45 (page 767)

Simplify:
$(a) \sqrt{\frac{80 m^{3}}{n^{6}}} (b) \sqrt[3]{\frac{108 c^{10}}{d^{6}}} (c) \sqrt[4]{\frac{80 x^{10}}{y^{4}}} .$

Short Answer

Expert verified

Part a. After simplifying we get, $\frac{4 m \sqrt{5 m}}{n^{3}} .$

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

Part c. After simplifying we get, $\frac{2 x^{2} \sqrt[4]{5 x^{2}}}{y} .$

Step by step solution

Part a Step 1. Given Information

The given expression is $\sqrt{\frac{80 m^{3}}{n^{6}}} .$

We have to simplify it.

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

Thus, we write $\sqrt{\frac{80 m^{3}}{n^{6}}}$ as $\frac{\sqrt{80 m^{3}}}{n^{6}} .$

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

After simplifying we get,

$\frac{\sqrt{80 m^{3}}}{\sqrt{n^{6}}} = \frac{\sqrt{{(4 m)}^{2}} \cdot \sqrt{5 m}}{\sqrt{{(n^{3})}^{2}}} = \frac{4 m \sqrt{5 m}}{n^{3}}$

Part b Step 1. Given Information

The given expression is $\sqrt[3]{\frac{108 c^{10}}{d^{6}}} .$

We have to simplify it.

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

Thus, we write $\sqrt[3]{\frac{108 c^{10}}{d^{6}}}$ as $\frac{\sqrt[3]{108 c^{10}}}{\sqrt[3]{d^{6}}} .$

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

After simplifying we get,

$\frac{\sqrt[3]{108 c^{10}}}{\sqrt[3]{d^{6}}} = \frac{\sqrt[3]{{(3 c^{3})}^{3}} \cdot \sqrt[3]{4 c}}{\sqrt[3]{{(d^{2})}^{3}}} = \frac{3 c^{3} \sqrt[3]{4 c}}{d^{2}}$

Part c Step 1. Given Information

The given expression is $\sqrt[4]{\frac{80 x^{10}}{y^{4}}} .$

We have to simplify it.

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

Thus, we write $\sqrt[4]{\frac{80 x^{10}}{y^{4}}}$ as $\frac{\sqrt[4]{80 x^{10}}}{\sqrt[4]{y^{4}}} .$

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

After simplifying we get,

$\frac{\sqrt[4]{80 x^{10}}}{\sqrt[4]{y^{4}}} = \frac{\sqrt[4]{{(2 x^{2})}^{4}} \cdot \sqrt[4]{5 x^{2}}}{y} = \frac{2 x^{2} \sqrt[4]{5 x^{2}}}{y}$

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Simplify:
$(a) \sqrt{\frac{80 m^{3}}{n^{6}}} (b) \sqrt[3]{\frac{108 c^{10}}{d^{6}}} (c) \sqrt[4]{\frac{80 x^{10}}{y^{4}}} .$

Short Answer

Step by step solution

Part a Step 1. Given Information

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. Given Information

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. Given Information

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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Simplify:a80m3n6b108c10d63c80x10y44.

Short Answer

Step by step solution

Part a Step 1. Given Information

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. Given Information

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. Given Information

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

Mechanics Maths

Pure Maths

Geometry

Calculus

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

Simplify:
$(a) \sqrt{\frac{80 m^{3}}{n^{6}}} (b) \sqrt[3]{\frac{108 c^{10}}{d^{6}}} (c) \sqrt[4]{\frac{80 x^{10}}{y^{4}}} .$