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Find the smallest number $y$ such that $y \times 162$ is a perfect cube.

1. $24$
2. $27$
3. $32$
4. $36$

edited | 1.9k views

$y \times 162 = y \times 3^4 \times 2$

So, for perfect cube we need to add two $3s$ and two $2s.$

Answer is: $3^2 \times 2^2= 36.$

Correct Answer: $D$
by (341 points)
edited

162 = 2 * 33 * 3

hence we can see the value which have two 2's and 2 3's wil be minimum value = 4 * 9 = 36 so option 4

by Boss (11.3k points)
Ans. 36

Factorization of 162 = 2*9*9

So, multiply by 2*2*9 to make perfect cube
by Active (1.1k points)
very easy just putting the options as the value of Y we get 36

so D is the correct answer i guess
by Boss (18k points)
+2
putting option is time consuming , just factorize everything is clear.