About Rationalize the Denominator:
When working with radicals, we always want to report a simplified result. One rule of simplification states that we can’t have a radical in the denominator. In order to deal with this problem, we follow a procedure known as rationalizing the denominator. This will give us a rational number in the denominator.
Test Objectives
- Demonstrate the ability to simplify a square root, cube root, or higher-level root
- Demonstrate the ability to rationalize a denominator that contains a square root
- Demonstrate the ability to rationalize a denominator that contains a cube root, or higher-level root
#1:
Instructions: Simplify each.
a) $$\frac{\sqrt{4}}{\sqrt{6}}$$
b) $$\frac{\sqrt{8}}{4\sqrt{6}}$$
c) $$\frac{\sqrt{5}}{6\sqrt{8}}$$
Watch the Step by Step Video Solution View the Written Solution
#2:
Instructions: Simplify each.
a) $$\frac{3\sqrt{5}}{5\sqrt{7}}$$
b) $$\frac{\sqrt{2}}{\sqrt{7}}$$
c) $$\frac{\sqrt{49}}{3\sqrt{14}}$$
Watch the Step by Step Video Solution View the Written Solution
#3:
Instructions: Simplify each.
a) $$\frac{\sqrt{32}}{\sqrt{20}}$$
b) $$\frac{\sqrt{3}}{4\sqrt{5}}$$
c) $$\frac{\sqrt{10}}{\sqrt{15}}$$
Watch the Step by Step Video Solution View the Written Solution
#4:
Instructions: Simplify each.
a) $$\frac{8\sqrt{10}+ \sqrt{5}}{\sqrt{13}}$$
b) $$\frac{5 + 4\sqrt{3}}{10\sqrt{31}}$$
Watch the Step by Step Video Solution View the Written Solution
#5:
Instructions: Simplify each.
a) $$\frac{3}{\sqrt[3]{3x}}$$
b) $$\frac{u}{\sqrt[4]{216u}}$$
Watch the Step by Step Video Solution View the Written Solution
Written Solutions:
#1:
Solutions:
a) $$\frac{\sqrt{6}}{3}$$
b) $$\frac{\sqrt{3}}{6}$$
c) $$\frac{\sqrt{10}}{24}$$
Watch the Step by Step Video Solution
#2:
Solutions:
a) $$\frac{3\sqrt{35}}{35}$$
b) $$\frac{\sqrt{14}}{7}$$
c) $$\frac{\sqrt{14}}{6}$$
Watch the Step by Step Video Solution
#3:
Solutions:
a) $$\frac{2\sqrt{10}}{5}$$
b) $$\frac{\sqrt{15}}{20}$$
c) $$\frac{\sqrt{6}}{3}$$
Watch the Step by Step Video Solution
#4:
Solutions:
a) $$\frac{8\sqrt{130}+ \sqrt{65}}{13}$$
b) $$\frac{5\sqrt{31}+ 4\sqrt{93}}{310}$$
Watch the Step by Step Video Solution
#5:
Solutions:
a) $$\frac{\sqrt[3]{9x^2}}{x}$$
b) $$\frac{\sqrt[4]{6u^3}}{6}$$
