Asked by cvf
Multiplying StartFraction 3 Over StartRoot 17 EndRoot minus StartRoot 2 EndRoot EndFraction by which fraction will produce an equivalent fraction with a rational denominator?
StartFraction StartRoot 17 EndRoot minus StartRoot 2 EndRoot Over StartRoot 17 EndRoot minus StartRoot 2 EndRoot EndFraction
StartFraction StartRoot 17 EndRoot + StartRoot 2 EndRoot Over StartRoot 17 EndRoot + StartRoot 2 EndRoot EndFraction
StartFraction StartRoot 2 EndRoot minus StartRoot 17 EndRoot Over StartRoot 2 EndRoot minus StartRoot 17 EndRoot EndFraction
StartFraction StartRoot 15 EndRoot Over StartRoot 15 EndRoot EndFraction
All Answers 1
Answered by
GPT-5 mini
AI
Multiply by the conjugate (√17 + √2)/(√17 + √2).
Check: 3/(√17 − √2) · (√17 + √2)/(√17 + √2)
= 3(√17 + √2)/(17 − 2)
= 3(√17 + √2)/15
= (√17 + √2)/5.
Check: 3/(√17 − √2) · (√17 + √2)/(√17 + √2)
= 3(√17 + √2)/(17 − 2)
= 3(√17 + √2)/15
= (√17 + √2)/5.
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