find the smallest number by which 17496 must be divided, so that the quotient is a perfect cube. Also find the cube root of the quotient
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Step-by-step explanation:
17496=8×2187
=8×9×243
=8×9×9×27
=(2^3)×(3^4)×(3^3)
=(2^3)×(3^3)×(3^3)×3
={(2×3×3)^3}×3
=18^3×3
If this number is divided by 3 we will get a perfect cube.....(18)^3
Quotient=18^3
Cube root of quotient=³√(18^3)=18
Answered by
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Answer:
17496=8×2187
=8×9×243
=8×9×9×27
=(2^3)×(3^4)×(3^3)
=(2^3)×(3^3)×(3^3)×3
={(2×3×3)^3}×3
=18^3×3
If the number is divided by 3 we will get a perfect cube(18)^3
Quotient=18^3
Cube root of =³√(18^3)=18
Step-by-step explanation:
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