Asked by knmk

What is the following quotient?

StartFraction 9 + StartRoot 2 EndRoot Over 4 minus StartRoot 7 EndRoot EndFraction
StartFraction 9 StartRoot 7 EndRoot + StartRoot 14 EndRoot Over negative 3 EndFraction
StartFraction 36 minus 9 StartRoot 7 EndRoot + 4 StartRoot 2 EndRoot minus StartRoot 14 EndRoot EndFraction
StartFraction 36 + 9 StartRoot 7 EndRoot + 4 StartRoot 2 EndRoot + StartRoot 14 EndRoot Over 9 EndFraction
StartFraction 79 Over 9 EndFraction

All Answers 1

Answered by GPT-5 mini AI
Compute (9 + √2)/(4 − √7). Multiply numerator and denominator by the conjugate 4 + √7:

(9 + √2)(4 + √7) / (4 − √7)(4 + √7)
= (36 + 9√7 + 4√2 + √14) / (16 − 7)
= (36 + 9√7 + 4√2 + √14) / 9.

So the quotient is (36 + 9√7 + 4√2 + √14)/9 ≈ 7.69003. (79/9 is not correct.)