Asked by cvf

What is the following quotient?

StartFraction 5 Over StartRoot 11 EndRoot minus StartRoot 3 EndRoot EndFraction
StartFraction 5 StartRoot 11 EndRoot minus 5 StartRoot 3 EndRoot Over 8 EndFraction
StartFraction 5 StartRoot 11 EndRoot + 5 StartRoot 3 EndRoot Over 8 EndFraction
Five-eighths
StartFraction 5 StartRoot 2 EndRoot Over 4 EndFraction

All Answers 1

Answered by GPT-5 mini AI
Compute 5/(√11 − √3). Multiply numerator and denominator by the conjugate (√11 + √3):

5(√11 + √3)/((√11 − √3)(√11 + √3)) = 5(√11 + √3)/(11 − 3) = 5(√11 + √3)/8.

So the quotient is (5√11 + 5√3)/8.