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krek1111 [17]
3 years ago
8

What is the following quotient? StartFraction StartRoot 6 EndRoot + StartRoot 11 EndRoot Over StartRoot 5 EndRoot + StartRoot 3

EndRoot EndFraction StartFraction StartRoot 30 EndRoot + 3 StartRoot 2 EndRoot + StartRoot 55 EndRoot + StartRoot 33 EndRoot Over 8 EndFraction StartFraction StartRoot 30 EndRoot minus 3 StartRoot 2 EndRoot + StartRoot 55 EndRoot minus StartRoot 33 EndRoot Over 2 EndFraction Seventeen-eighths Negative five-halves
Mathematics
2 answers:
Katen [24]3 years ago
6 0

Answer:

Option C on Edge2020.

Step-by-step explanation:

Delicious77 [7]3 years ago
5 0

Answer:

<h3>StartFraction StartRoot 30 EndRoot minus 3 StartRoot 2 EndRoot + StartRoot 55 EndRoot minus StartRoot 33 EndRoot Over 2</h3>

Step-by-step explanation:

Given the surdic equation as shown \frac{\sqrt{6}+\sqrt{11}  }{\sqrt{5}+\sqrt{3} }\\

To find the quotient, we will rationalize by multipying both numerator and denominator of the function by the conjugate of the denominator.

Given the denominator \sqrt{5}+\sqrt{3}, its conjugate will be \sqrt{5}-\sqrt{3}

Multiplying through by \sqrt{5}-\sqrt{3}, we have;

= \frac{\sqrt{6}+\sqrt{11}  }{\sqrt{5}+\sqrt{3} } * \frac{\sqrt{5}-\sqrt{3}  }{\sqrt{5}-\sqrt{3} }\\

= \frac{\sqrt{30}- \sqrt{18}+\sqrt{55}-\sqrt{33}}{2}\\= \frac{\sqrt{30}- \sqrt{9*2}+\sqrt{55}-\sqrt{33}}{2}\\= \frac{\sqrt{30}- 3\sqrt{2}+\sqrt{55}-\sqrt{33}}{2}

The final expression gives the requires answer

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