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Radicand: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">RadicandRadicand: Definition and ExamplesTable of ContentsUnderstanding Radicand in Mathematics Definition of Radicand

A radicand is the number or expression that appears under the radical symbol (√). The radicand can be any real number, positive or negative, or it can also be an algebraic expression. The radical symbol (√) is used to denote the square root or the nth roots. In other words, the radicand is the value or quantity that you want to find the square root or the nth root of.

Radicands can be positive or negative, though we generally deal with positive radicand values. If the index (the small number at the top left of the radical symbol) is even, then we must consider only positive radicands to get real solutions. For example, we can solve 3−27=−3^3\sqrt{-27} = -33−27​=−3 since (−3)×(−3)×(−3)=−27(-3) \times (-3) \times (-3) = -27(−3)×(−3)×(−3)=−27. However, −4\sqrt{-4}−4​ doesn't have a real solution because a negative number multiplied by itself an even number of times will never give a negative result.

Examples of Radicand Usage Example 1: Identifying the Radicand in an Expression Problem:

From the given expression, identify the radicand: 38+27−b^{3}\sqrt{8} + 27-b38​+27−b.

Step-by-step solution:

Step 1, Look at the expression carefully to find any terms with radical symbols. In 38+27−b^{3}\sqrt{8} + 27-b38​+27−b, only 38^{3}\sqrt{8}38​ involves a radical symbol.

Step 2, Find what's under the radical symbol. In 38^{3}\sqrt{8}38​, the number 888 is written under the radical symbol.

Step 3, Since 888 is the number under the radical symbol, 888 is the radicand in the given expression.

Example 2: Simplifying an Expression with Radicals Problem:

Simplify the given expression: 128×32\sqrt{128} \times \sqrt{32}128​×32​.

Step-by-step solution:

Step 1, Apply the formula x×y=x×y\sqrt{x} \times \sqrt{y} = \sqrt{x \times y}x​×y​=x×y​ to combine the radicals: 128×32=128×32\sqrt{128} \times \sqrt{32} = \sqrt{128 \times 32}128​×32​=128×32​

Step 2, Multiply the radicands: 128×32=4,096\sqrt{128 \times 32} = \sqrt{4,096}128×32​=4,096​

Step 3, Find a perfect square to simplify the radicand: 4,096=64×64\sqrt{4,096} = \sqrt{64 \times 64}4,096​=64×64​

Step 4, Calculate the square root of the perfect square: 64×64=64\sqrt{64 \times 64} = 6464×64​=64

Step 5, So, 128×32=64\sqrt{128} \times \sqrt{32} = 64128​×32​=64

Example 3: Identifying Radicand and Index in an Expression Problem:

Identify the radicand and index in the expression 8132^{8}\sqrt{13^{2}}8132​.

Step-by-step solution:

Step 1, Calculate the value inside the radical symbol: 132=16913^{2} = 169132=169, so 8132=8169^{8}\sqrt{13^{2}} = ^{8}\sqrt{169}8132​=8169​

Step 2, Find the index, which is the small number on the top left of the radical sign. In this expression, the index is 888.

Step 3, Find the radicand, which is the expression inside the radical symbol. In this case, the radicand is 13213^{2}132 or 169.

Step 4, So in the expression 8132^{8}\sqrt{13^{2}}8132​, the index is 888 and the radicand is 132=16913^{2} = 169132=169.

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