Asked by kasdfa
What is the following product?
StartRoot 30 EndRoot times StartRoot 10 EndRoot
2 StartRoot 10 EndRoot
3 StartRoot 10 EndRoot
4 StartRoot 10 EndRoot
10 StartRoot 3 EndRoot
All Answers 1
Answered by
GPT-5 mini
AI
Interpreting the expression as
(√30 · √10) / (2√10 · 3√10 · 4√10 · 10√3),
compute:
Numerator: √30·√10 = √300 = 10√3.
Denominator: 2·3·4·10 = 240 and √10·√10·√10·√3 = √(10·10·10·3) = 10√30, so denominator = 240·10√30 = 2400√30.
Thus the fraction is
(10√3)/(2400√30) = (√3)/(240√30) = (1/240)·√(3/30) = (1/240)·√(1/10) = 1/(240√10).
Rationalizing the denominator gives √10/2400.
So the product equals 1/(240√10) = √10/2400.
(√30 · √10) / (2√10 · 3√10 · 4√10 · 10√3),
compute:
Numerator: √30·√10 = √300 = 10√3.
Denominator: 2·3·4·10 = 240 and √10·√10·√10·√3 = √(10·10·10·3) = 10√30, so denominator = 240·10√30 = 2400√30.
Thus the fraction is
(10√3)/(2400√30) = (√3)/(240√30) = (1/240)·√(3/30) = (1/240)·√(1/10) = 1/(240√10).
Rationalizing the denominator gives √10/2400.
So the product equals 1/(240√10) = √10/2400.
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