Select the answer which is equivalent to the given expression using your calculator. (-16)/(20+sqrt8) (-40+2sqrt8)/(7) (-40-2sqrt8)/(49) (-40+2sqrt8)/(49) (-40-2sqrt8)/(7)

Simplify Square Root: Simplify the square root in the denominator of the original expression. Evaluate sqrt(8). sqrt(8) = sqrt(4 * 2) = sqrt(4) * sqrt(2) = 2 * sqrt(2)Substitute Simplified Expression: Substitute the simplified square root back into the original expression. The original expression becomes (-16)/(20 + 2 * sqrt(2)).Find Equivalent Expression: Look for the expression that matches the simplified original expression. We need to find an expression that is equivalent to (-16)/(20 + 2 * sqrt(2)).Check Answer Choices: Check each answer choice to see if it simplifies to (-16)/(20 + 2 * sqrt(2)). We can eliminate any choices that do not have a denominator of (20 + 2 * sqrt(2)) or an equivalent expression.First Choice Equivalent: The first choice (-16)/(20+sqrt8) is the original expression, so it is equivalent.The second choice (-40+2sqrt8)/(7) does not have the same denominator as our simplified original expression, so it is not equivalent.The third choice (-40-2sqrt8)/(49) does not have the same denominator as our simplified original expression, so it is not equivalent.The fourth choice (-40+2sqrt8)/(49) does not have the same denominator as our simplified original expression, so it is not equivalent.The fifth choice (-40-2sqrt8)/(7) does not have the same denominator as our simplified original expression, so it is not equivalent.Conclude that the first choice is the only equivalent expression. The equivalent expression to (-16)/(20+sqrt8) is itself, which is the first choice.

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Select the answer which is equivalent to the given expression using your calculator.

(-16)/(20+sqrt8)

(-40+2sqrt8)/(7)

(-40-2sqrt8)/(49)

(-40+2sqrt8)/(49)

(-40-2sqrt8)/(7)

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\frac{-16}{20+\sqrt{8}}$ $\newline$ $\frac{-40+2 \sqrt{8}}{7}$ $\newline$ $\frac{-40-2 \sqrt{8}}{49}$ $\newline$ $\frac{-40+2 \sqrt{8}}{49}$ $\newline$ $\frac{-40-2 \sqrt{8}}{7}$

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Q. Select the answer which is equivalent to the given expression using your calculator.

\newline

\frac{-16}{20+\sqrt{8}}

\newline

\frac{-40+2 \sqrt{8}}{7}

\newline

\frac{-40-2 \sqrt{8}}{49}

\newline

\frac{-40+2 \sqrt{8}}{49}

\newline

\frac{-40-2 \sqrt{8}}{7}

Simplify Square Root: Simplify the square root in the denominator of the original expression. $\newline$ Evaluate $\sqrt{8}$ . $\newline$ $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2 \times \sqrt{2}$
Substitute Simplified Expression: Substitute the simplified square root back into the original expression. $\newline$ The original expression becomes $(-16)/(20 + 2 \cdot \sqrt{2})$ .
Find Equivalent Expression: Look for the expression that matches the simplified original expression. $\newline$ We need to find an expression that is equivalent to $(-16)/(20 + 2 \cdot \sqrt{2})$ .
Check Answer Choices: Check each answer choice to see if it simplifies to $(-16)/(20 + 2 \sqrt{2})$ . We can eliminate any choices that do not have a denominator of $(20 + 2 \sqrt{2})$ or an equivalent expression.
First Choice Equivalent: The first choice $-\frac{16}{20+\sqrt{8}}$ is the original expression, so it is equivalent.
First Choice Equivalent: The first choice $(-16)/(20+\sqrt{8})$ is the original expression, so it is equivalent.The second choice $(-40+2\sqrt{8})/(7)$ does not have the same denominator as our simplified original expression, so it is not equivalent.
First Choice Equivalent: The first choice $(-16)/(20+\sqrt{8})$ is the original expression, so it is equivalent.The second choice $(-40+2\sqrt{8})/(7)$ does not have the same denominator as our simplified original expression, so it is not equivalent.The third choice $(-40-2\sqrt{8})/(49)$ does not have the same denominator as our simplified original expression, so it is not equivalent.
First Choice Equivalent: The first choice $(-16)/(20+\sqrt{8})$ is the original expression, so it is equivalent.The second choice $(-40+2\sqrt{8})/(7)$ does not have the same denominator as our simplified original expression, so it is not equivalent.The third choice $(-40-2\sqrt{8})/(49)$ does not have the same denominator as our simplified original expression, so it is not equivalent.The fourth choice $(-40+2\sqrt{8})/(49)$ does not have the same denominator as our simplified original expression, so it is not equivalent.
First Choice Equivalent: The first choice $(-16)/(20+\sqrt{8})$ is the original expression, so it is equivalent.The second choice $(-40+2\sqrt{8})/(7)$ does not have the same denominator as our simplified original expression, so it is not equivalent.The third choice $(-40-2\sqrt{8})/(49)$ does not have the same denominator as our simplified original expression, so it is not equivalent.The fourth choice $(-40+2\sqrt{8})/(49)$ does not have the same denominator as our simplified original expression, so it is not equivalent.The fifth choice $(-40-2\sqrt{8})/(7)$ does not have the same denominator as our simplified original expression, so it is not equivalent.
First Choice Equivalent: The first choice $(-16)/(20+\sqrt{8})$ is the original expression, so it is equivalent.The second choice $(-40+2\sqrt{8})/(7)$ does not have the same denominator as our simplified original expression, so it is not equivalent.The third choice $(-40-2\sqrt{8})/(49)$ does not have the same denominator as our simplified original expression, so it is not equivalent.The fourth choice $(-40+2\sqrt{8})/(49)$ does not have the same denominator as our simplified original expression, so it is not equivalent.The fifth choice $(-40-2\sqrt{8})/(7)$ does not have the same denominator as our simplified original expression, so it is not equivalent.Conclude that the first choice is the only equivalent expression. $\newline$ The equivalent expression to $(-16)/(20+\sqrt{8})$ is itself, which is the first choice.