Simplifying Radicals and Radical Operations

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What is a radical?

Back

Tags

CCSS.8.NS.A.1

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What does it mean to simplify a radical?

Back

To simplify a radical means to express it in its simplest form, removing any perfect square factors from under the radical sign.

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Back

@@\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}$$.

Front

What is the product of two radicals?

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The product of two radicals can be simplified by multiplying the numbers under the radicals together. For example, @@\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$$.

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How do you add radicals?

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You can only add radicals that have the same radicand (the number under the radical). For example, @@2\sqrt{3} + 3\sqrt{3} = 5\sqrt{3}$$.

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The sum is @@\sqrt{7}$$.

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How do you multiply a radical by a whole number?

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To multiply a radical by a whole number, simply multiply the whole number by the coefficient of the radical. For example, @@2\sqrt{5} \cdot 3 = 6\sqrt{5}$$.

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The area is @@16\sqrt{6}$$.

Tags

CCSS.7.EE.B.3

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The cube root is @@2r^2s\cdot \sqrt[3]{7r^2s}$$.

Front

What is the formula for the area of a rectangle?

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The area of a rectangle is calculated by multiplying its length by its width: Area = Length × Width.

Tags

CCSS.3.MD.C.7B

CCSS.4.MD.A.3