About Simplifying Radicals:
We simplify radicals using the product/quotient rule for radicals. This rule allows us to break the radicand up and pull out rational numbers. For example, we can break up the square root of 20 into: the square root of 5 times the square root of 4. The square root of 4 represents a rational number 2. We report our simplified radical as 2 times the square root of 5.
Test Objectives
- Demonstrate the ability to use the product rule for radicals
- Demonstrate the ability to use the quotient rule for radicals
- Demonstrate the ability to simplify a radical
#1:
Instructions: Simplify each, all variables are positive real numbers.
a) $$\sqrt[3]{-625}$$
b) $$\sqrt[5]{96}$$
c) $$\sqrt[4]{162}$$
Watch the Step by Step Video Solution View the Written Solution
#2:
Instructions: Simplify each, all variables are positive real numbers.
a) $$-2\sqrt{147p^4}$$
b) $$-5\sqrt{90x^4}$$
Watch the Step by Step Video Solution View the Written Solution
#3:
Instructions: Simplify each, all variables are positive real numbers.
a) $$3\sqrt[5]{192x^7y^4z^8}$$
b) $$6\sqrt[4]{160x^4yz^9}$$
Watch the Step by Step Video Solution View the Written Solution
#4:
Instructions: Simplify each, all variables are positive real numbers.
a) $$\frac{4\sqrt[4]{20}}{3\sqrt[4]{1024}}$$
b) $$\frac{3\sqrt[5]{-2}}{5\sqrt[5]{3125}}$$
Watch the Step by Step Video Solution View the Written Solution
#5:
Instructions: Simplify each, all variables are positive real numbers.
a) $$\sqrt{10}\cdot \sqrt[6]{9}$$
Watch the Step by Step Video Solution View the Written Solution
Written Solutions:
#1:
Solutions:
a) $$-5\sqrt[3]{5}$$
b) $$2\sqrt[5]{3}$$
c) $$3\sqrt[4]{2}$$
Watch the Step by Step Video Solution
#2:
Solutions:
a) $$-14p^2\sqrt{3}$$
b) $$-15x^2\sqrt{10}$$
Watch the Step by Step Video Solution
#3:
Solutions:
a) $$6xz\sqrt[5]{6x^2y^4z^3}$$
b) $$12xz^2\sqrt[4]{10yz}$$
Watch the Step by Step Video Solution
#4:
Solutions:
a) $$\frac{\sqrt[4]{5}}{3}$$
b) $$\frac{-3\sqrt[5]{2}}{25}$$
Watch the Step by Step Video Solution
#5:
Solutions:
a) $$\sqrt[6]{9000}$$