About Simplifying Radical Expressions:
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.
Assume all variables are positive real numbers.
$$a)\hspace{.2em}\sqrt{96x}$$
$$b)\hspace{.2em}\sqrt{180x^3}$$
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#2:
Instructions: Simplify each.
Assume all variables are positive real numbers.
$$a)\hspace{.2em}\sqrt[7]{512x^2}$$
$$b)\hspace{.2em}\sqrt[4]{80x^7}$$
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#3:
Instructions: Simplify each.
Assume all variables are positive real numbers.
$$a)\hspace{.2em}4\sqrt[3]{320x^8y^3}$$
$$b)\hspace{.2em}{-}6\sqrt[3]{64xy^5}$$
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#4:
Instructions: Simplify each.
Assume all variables are positive real numbers.
$$a)\hspace{.2em}{-}2\sqrt[3]{375x^2y^4z^8}$$
$$b)\hspace{.2em}{-}5\sqrt{72x^4yz^2}$$
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#5:
Instructions: Simplify each.
Assume all variables are positive real numbers.
$$a)\hspace{.2em}\sqrt[5]{\sqrt[9]{2x}}$$
$$b)\hspace{.2em}\sqrt[5]{\sqrt{x + 1}}$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}4 \sqrt{6x}$$
$$b)\hspace{.2em}6x \sqrt{5x}$$
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#2:
Solutions:
$$a)\hspace{.2em}2 \sqrt[7]{4x^2}$$
$$b)\hspace{.2em}2x \sqrt[4]{5x^3}$$
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#3:
Solutions:
$$a)\hspace{.2em}16x^2y\sqrt[3]{5x^2}$$
$$b)\hspace{.2em}{-}24y\sqrt[3]{xy^2}$$
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#4:
Solutions:
$$a)\hspace{.2em}{-}10yz^2\sqrt[3]{3x^2yz^2}$$
$$b)\hspace{.2em}{-}30x^2z\sqrt{2y}$$
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#5:
Solutions:
$$a)\hspace{.2em}\sqrt[45]{2x}$$
$$b)\hspace{.2em}\sqrt[10]{x + 1}$$
