Test Objectives
• Demonstrate an understanding of "like radicals"
• Demonstrate the ability to subtract radical expressions
• Demonstrate the ability to multiply radical expressions
Operations with Radical Expressions Practice Test:

#1:

Instructions: Simplify each.

Assume all variables are positive real numbers.

$$a)\hspace{.2em}3\sqrt{54}- 3\sqrt{24}$$

$$b)\hspace{.2em}-x\sqrt[3]{24x}+ 3\sqrt[3]{3x^4}$$

#2:

Instructions: Simplify each.

Assume all variables are positive real numbers.

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$$a)\hspace{.2em}-2\sqrt[4]{80x^5}+ 2x\sqrt[4]{405x}+ 2x\sqrt[4]{324}$$

$$b)\hspace{.2em}2xy\sqrt[3]{8xyz}+ \sqrt[3]{x^4y^4z}$$

#3:

Instructions: Simplify each.

Assume all variables are positive real numbers.

$$a)\hspace{.2em}3\sqrt{15}(4 + \sqrt{5})$$

$$b)\hspace{.2em}2\sqrt{20}\cdot 5 \sqrt{5}$$

#4:

Instructions: Simplify each.

Assume all variables are positive real numbers.

$$a)\hspace{.2em}(\sqrt{3}- 5)(\sqrt{3}+ 5)$$

$$b)\hspace{.2em}(4\sqrt{3x}+ 4)(4\sqrt{3x}- 4)$$

#5:

Instructions: Simplify each.

Assume all variables are positive real numbers.

$$a)\hspace{.2em}(5\sqrt{3}+ 2)(2\sqrt{3}+ 3)$$

$$b)\hspace{.2em}(2x + \sqrt[3]{y})(4x + 5\sqrt[3]{y})$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}3\sqrt{6}$$

$$b)\hspace{.2em}x \cdot \sqrt[3]{3x}$$

#2:

Solutions:

$$a)\hspace{.2em}2x \cdot \sqrt[4]{5x}+ 6x \cdot \sqrt{2}$$

$$b)\hspace{.2em}5xy \cdot \sqrt[3]{xyz}$$

#3:

Solutions:

$$a)\hspace{.2em}12\sqrt{15}+ 15\sqrt{3}$$

$$b)\hspace{.2em}100$$

#4:

Solutions:

$$a)\hspace{.2em}-22$$

$$b)\hspace{.2em}48x-16$$

#5:

Solutions:

$$a)\hspace{.2em}36 + 19 \sqrt{3}$$

$$b)\hspace{.2em}8x^2 + 14x \sqrt[3]{y}+ 5\sqrt[3]{y^2}$$