Question

Solve for $Y.$

$\sqrt[3]{36125\times \left(Y\right)}=35$

• A. 14
• B. 35
• C. 7
• D. 21

Answer 1

The correct option is C

7

Here in expression $\sqrt[3]{36125\times \left(Y\right)}=35$,

we can see thatcube root of $6125\times \left(Y\right)$ is equal to 35, which implies cube of 35 is equal to $6125\times \left(Y\right).$

Hence, $6125\times \left(Y\right)$ = ${35}^3$

So, $6125\times \left(Y\right)=42875$

$Y=\frac{42875}{6125}$

$Y=7$

Alternate Solution,

By Prime factorization of 6125 , we get $6125=5\times 5\times 5\times 7\times 7$

Hence $\sqrt[3]{36125=5\times 5\times 5\times 7\times 7\times \left(Y\right)}=35$

To get a perfect cube , we need to have the triplet of the prime factor .

Given that cube root of 6125 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 6125 and 7 , it becomes a perfect cube .

$\sqrt[3]{36125=5\times 5\times 5\times 7\times 7\times \left(Y\right)}$ = $\sqrt[3]{36125=5\times 5\times 5\times 7\times 7\times \left(7\right)}=35$

$\therefore Y=7$