About Rationalizing the Denominator:
A simplified radical expression does not contain any radicals in the denominator. The process we use to clear a denominator of its radical is known as rationalizing the denominator. We rationalize the denominator by multiplying the numerator and denominator by a radical that will transform the denominator into a rational number.
Test Objectives
- Demonstrate the ability to multiply radicals
- Demonstrate the ability to rationalize a denominator with a square root
- Demonstrate the ability to rationalize a denominator with a higher level root
#1:
Instructions: Simplify each.
a) $$\frac{11\sqrt{10}}{8\sqrt{7}}$$
b) $$\frac{2\sqrt{24}}{2\sqrt{56}}$$
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#2:
Instructions: Simplify each.
a) $$\frac{2\sqrt[3]{3}}{5\sqrt[3]{9}}$$
b) $$\frac{3\sqrt[3]{5x^4y}}{4\sqrt[3]{2x^3y^3}}$$
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#3:
Instructions: Simplify each.
a) $$\frac{5x^2 - 2\sqrt{x^4}}{5\sqrt{12x^3}}$$
b) $$\frac{5\sqrt{3p}- 5\sqrt{2p^2}}{3\sqrt{10p}}$$
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#4:
Instructions: Simplify each.
a) $$\frac{3x + 3\sqrt[3]{2x^3}}{3\sqrt[3]{4x^2}}$$
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#5:
Instructions: Simplify each.
a) $$\frac{-5p + 2\sqrt[4]{3p^3}}{4\sqrt[4]{12p}}$$
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Written Solutions:
#1:
Solutions:
a) $$\frac{11\sqrt{70}}{56}$$
b) $$\frac{\sqrt{21}}{7}$$
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#2:
Solutions:
a) $$\frac{2\sqrt[3]{9}}{15}$$
b) $$\frac{3\sqrt[3]{20xy}}{8y}$$
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#3:
Solutions:
a) $$\frac{\sqrt{3x}}{{10}}$$
b) $$\frac{\sqrt{30}- 2\sqrt{5p}}{6}$$
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#4:
Solutions:
a) $$\frac{\sqrt[3]{2x}+ \sqrt[3]{4x}}{2}$$
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#5:
Solutions:
a) $$\frac{-5\sqrt[4]{108p^3}+ 6\sqrt{2p}}{24}$$
