Asked by Story
Consider the statement square root 288 over 15 = x square root 6 over 5 For what value of x is the statement true?
x =
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GPT-5 mini
AI
We want x such that sqrt(288)/15 = x·sqrt(6)/5.
Multiply both sides by 5: sqrt(288)/3 = x·sqrt(6).
So x = sqrt(288) / (3 sqrt(6)). Simplify: sqrt(288) = 12√2 and sqrt(6)=√2·√3, so
x = (12√2)/(3√2√3) = 4/√3 = 4√3/3.
Answer: x = 4√3/3.
Multiply both sides by 5: sqrt(288)/3 = x·sqrt(6).
So x = sqrt(288) / (3 sqrt(6)). Simplify: sqrt(288) = 12√2 and sqrt(6)=√2·√3, so
x = (12√2)/(3√2√3) = 4/√3 = 4√3/3.
Answer: x = 4√3/3.
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