AnswersAdv. Algebra II S2 OriginalRational Exponents

Adding and Subtracting Radicals Answers

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Which of the following are like radicals? Check all of the boxes that apply.

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Which is a like radical to after simplifying?

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What is the radical part of both [image 1] and [image 2] when the expressions are simplified?

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Which expression equals ?

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Find the sum .

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Find the difference:

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Simplify the following expression completely, where x [image 1] 0. [image 2]

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Use the for d =

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⇒ 2

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2

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⇒ 6

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6

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What is the student’s error?

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The student should not have multiplied each expression by two.
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The student simplified incorrectly.
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The student simplified incorrectly.
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The student incorrectly simplified .
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Given that [image 1] is it ever possible to have [image 2] Explain.

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Yes. It is possible when one radicand is zero and the other is nonzero. For example, if a = 0 and b = 1, then √a + √b = 0 + 1 = 1 = √(a + b), even though a ≠ b.

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Which of the following did you include in your response?

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Yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.
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If either a or b equals zero, then the sums would be the same.
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Since the square root of 0 is 0, adding it to a given radical would not change the radical. Also, adding zero to the radicand would not change its value.
15

Three radical expressions have different radicands and, when simplified, are like radicals to .Describe key characteristics of these radical expressions.

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Each expression is a square root. Its radicand has a numerical coefficient equal to 3 times a perfect square, and both x and y have odd exponents. After taking out perfect-square factors, the remaining radical is √(3xy).

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Which of the following did you include in your description?

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The index is 2.
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The numeric coefficient of the radicand is three times a perfect-square number.
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The variable x in the radicand is raised to an odd power
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The variable y in the radicand is raised to an odd power.

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