Now that we can multiply, divide, and simplify radicals, our next step is to learn addition and subtraction. When we perform addition or subtraction with radicals, we must first ensure that we have “like radicals”. Like radicals have the index and the same radicand.

Test Objectives
• Demonstrate the ability to simplify a square root, cube root, or higher-level root
• Demonstrate the ability to add two or more roots
• Demonstrate the ability to subtract roots

#1:

Instructions: Perform each operation and simplify.

a) $$-4\sqrt{3}- 3\sqrt{3}$$

b) $$3\sqrt{7}- 3\sqrt{7}$$

c) $$-3\sqrt{8}+ 2\sqrt{8}$$

#2:

Instructions: Perform each operation and simplify.

a) $$2\sqrt{54}- 2\sqrt{20}- \sqrt{54}$$

b) $$-\sqrt{2}+ 2\sqrt{12}+ 3\sqrt{27}$$

#3:

Instructions: Perform each operation and simplify.

a) $$-\sqrt{24}- \sqrt{12}- 4\sqrt{18}+ 3\sqrt{24}$$

b) $$5\sqrt{75x^2}- 4\sqrt{27x^2}$$

c) $$3x\sqrt{24x^2y^2}+ 9y\sqrt{54x^3}$$

#4:

Instructions: Perform each operation and simplify.

a) $$4\sqrt{48}+ 3\sqrt{5}+ 4\sqrt{5}+ 2\sqrt{5}$$

b) $$2\sqrt{96}- 2\sqrt{96}- \sqrt{256}- 3\sqrt{405}$$

#5:

Instructions: Perform each operation and simplify.

a) $$-2\sqrt{-16}+ 2\sqrt{7}- \sqrt{4}+ 3\sqrt{16}$$

b) $$-\sqrt{448}- 4\sqrt{128}- 4\sqrt{7}- 3\sqrt{56}$$

Written Solutions:

#1:

Solutions:

a) $$-7\sqrt{3}$$

b) $$0$$

c) $$-2\sqrt{2}$$

#2:

Solutions:

a) $$3\sqrt{6}- 4\sqrt{5}$$

b) $$-\sqrt{2}+ 13\sqrt{3}$$

#3:

Solutions:

a) $$4\sqrt{6}- 2\sqrt{3}- 12\sqrt{2}$$

b) $$13x\sqrt{3}$$

c) $$6x^2y\sqrt{6}+ 27xy\sqrt{6x}$$

#4:

Solutions:

a) $$8\sqrt{6}+ 9\sqrt{5}$$

b) $$-2\sqrt{8}- 9\sqrt{5}$$

#5:

Solutions:

a) $$10\sqrt{2}+ 2\sqrt{7}- \sqrt{4}$$

b) $$-14\sqrt{7}- 16\sqrt{2}$$