Mathematics: 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

It’s called a trapezoidal prism because the two bases are trapezoids....

What is the following quotient? StartFraction StartRoot

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iisofieii1978

27.01.2022

Mathematics

StartFraction StartRoot 30 EndRoot minus 3 StartRoot 2 EndRoot + StartRoot 55 EndRoot minus StartRoot 33 EndRoot Over 2

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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