Select the answer which is equivalent to the given expression using your calculator. (-5)/(10+sqrt6) (-50-5sqrt6)/(94) (-350-35sqrt6)/(94) (-50+5sqrt6)/(94) (-350+35sqrt6)/(94)

Rationalize Denominator: To find the equivalent expression, we need to rationalize the denominator of the given expression (-5)/(10+sqrt6). This means we need to eliminate the square root from the denominator.Multiply by Conjugate: To rationalize the denominator, we multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of (10+sqrt6) is (10-sqrt6).Simplify Numerator: Now, multiply the numerator and the denominator by the conjugate: ((-5)/(10+sqrt6)) * ((10-sqrt6)/(10-sqrt6)) = (-5 * (10-sqrt6)) / ((10+sqrt6) * (10-sqrt6)).Simplify Denominator: Simplify the numerator: -5 * (10-sqrt6) = -50 + 5sqrt6.Final Simplified Expression: Simplify the denominator using the difference of squares formula: (10+sqrt6) * (10-sqrt6) = 10^2 - (sqrt6)^2 = 100 - 6 = 94.Compare with Answer Choices: Now we have the simplified expression: (-50 + 5sqrt6) / 94.Comparing the simplified expression with the answer choices, we find that the equivalent expression is (-50+5sqrt6)/(94).

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

(-5)/(10+sqrt6)

(-50-5sqrt6)/(94)

(-350-35sqrt6)/(94)

(-50+5sqrt6)/(94)

(-350+35sqrt6)/(94)

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\frac{-5}{10+\sqrt{6}}$ $\newline$ $\frac{-50-5 \sqrt{6}}{94}$ $\newline$ $\frac{-350-35 \sqrt{6}}{94}$ $\newline$ $\frac{-50+5 \sqrt{6}}{94}$ $\newline$ $\frac{-350+35 \sqrt{6}}{94}$

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Math Problems

Algebra 2

Sum of finite series starts from 1

Full solution

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

\newline

\frac{-5}{10+\sqrt{6}}

\newline

\frac{-50-5 \sqrt{6}}{94}

\newline

\frac{-350-35 \sqrt{6}}{94}

\newline

\frac{-50+5 \sqrt{6}}{94}

\newline

\frac{-350+35 \sqrt{6}}{94}

Rationalize Denominator: To find the equivalent expression, we need to rationalize the denominator of the given expression $(-5)/(10+\sqrt{6})$ . This means we need to eliminate the square root from the denominator.
Multiply by Conjugate: To rationalize the denominator, we multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of $(10+\sqrt{6})$ is $(10-\sqrt{6})$ .
Simplify Numerator: Now, multiply the numerator and the denominator by the conjugate: $\left(\frac{-5}{10+\sqrt{6}}\right) \times \left(\frac{10-\sqrt{6}}{10-\sqrt{6}}\right) = \frac{-5 \times (10-\sqrt{6})}{(10+\sqrt{6}) \times (10-\sqrt{6})}.$
Simplify Denominator: Simplify the numerator: $-5 \times (10-\sqrt{6}) = -50 + 5\sqrt{6}$ .
Final Simplified Expression: Simplify the denominator using the difference of squares formula: $(10+\sqrt{6}) \times (10-\sqrt{6}) = 10^2 - (\sqrt{6})^2 = 100 - 6 = 94$ .
Compare with Answer Choices: Now we have the simplified expression: $(-50 + 5\sqrt{6}) / 94$ .
Compare with Answer Choices: Now we have the simplified expression: $(-50 + 5\sqrt{6}) / 94$ .Comparing the simplified expression with the answer choices, we find that the equivalent expression is $(-50+5\sqrt{6})/(94)$ .