In order to add or subtract radicals, we must have “like radicals”. Like radicals have the same index along with the same radicand. This is similar to working with polynomials and looking for “like terms”. We add and subtract radicals using the distributive property. Essentially we only need to add or subtract the numbers multiplying the common radical.

Test Objectives
• Demonstrate the ability to identify like radicals
• Demonstrate the ability to simplify radicals

#1:

Instructions: Perform each indicated operation.

a) $$4\sqrt[3]{80} - 3\sqrt[3]{10} - 2\sqrt[3]{10}$$

b) $$2\sqrt[4]{144} + 2\sqrt[4]{9} - 15\sqrt[4]{9}$$

#2:

Instructions: Perform each indicated operation.

a) $$-4\sqrt[3]{320} + 5\sqrt[3]{5} - \sqrt[3]{625}$$

b) $$2\sqrt[3]{1250} + 2\sqrt[3]{32} - 2\sqrt[3]{270}$$

#3:

Instructions: Perform each indicated operation.

a) $$-2\sqrt[3]{1125} - 5\sqrt[3]{-72} - \sqrt[3]{54}$$

b) $$6\sqrt[5]{96} - \sqrt[5]{729} + 11\sqrt[5]{3072}$$

#4:

Instructions: Perform each indicated operation.

a) $$-\sqrt[6]{4} - 2\sqrt[6]{128} - \sqrt[6]{2} - 2\sqrt[6]{256}$$

#5:

Instructions: Perform each indicated operation.

a) $$2\sqrt[3]{2} - \sqrt[3]{24} + 2\sqrt[3]{16} - 2\sqrt[3]{3}$$

Written Solutions:

#1:

Solutions:

a) $$3\sqrt[3]{10}$$

b) $$-9\sqrt{3}$$

#2:

Solutions:

a) $$-16\sqrt[3]{5}$$

b) $$4\sqrt[3]{10} + 4\sqrt[3]{4}$$

#3:

Solutions:

a) $$-3\sqrt[3]{2}$$

b) $$53\sqrt[5]{3}$$

#4:

Solutions:

a) $$-5\sqrt[3]{2} - 5\sqrt[6]{2}$$

#5:

Solutions:

a) $$6\sqrt[3]{2} - 4\sqrt[3]{3}$$