    Question

# Solve for Y. 3√6,125×(Y)=35

A

14

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B

35

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C

7

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D

21

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Solution

## The correct option is C 7 Here in expression 3√6,125×(Y)=35, we can see that cube root of 6,125×(Y) is equal to 35, which implies cube of 35 is equal to 6,125×(Y). Hence, 6,125×(Y) = 353 So, 6,125×(Y)=42,875 Y=42,8756,125 Y=7 Alternate solution, By prime factorization of 6,125 , we get: 6,125=5×5×5×7×7 Hence,3√6,125×(Y)=35 ⇒ 3√5×5×5×7×7×(Y)=35 To get a perfect cube, we need to have the triplet of the prime factor. Given that cube root of 6,125 is multiplied by a number to get the perfect cube. In the factorization, we have 5 forming a triplet but not 7. Hence, when we multiply 6,125 and 7, it becomes a perfect cube. 3√6,125×(Y)=35 ⇒ 3√5×5×5×7×7×(Y)=35 ⇒3√5×5×5×7×7×(7)=35 ⇒ 3√6,125×(7)=35 ∴Y=7  Suggest Corrections  0      Similar questions
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