Question

Solve for $Y.$

$\sqrt[3]{36,125\times \left(Y\right)}=35$

• A. 14
• B. 35
• C. 7
• D. 21

Answer 1

The correct option is C

7

Here in expression $\sqrt[3]{36,125\times \left(Y\right)}=35$,

we can see that cube root of $6,125\times \left(Y\right)$ is equal to 35, which implies cube of 35 is equal to $6,125\times \left(Y\right).$

Hence, $6,125\times \left(Y\right)$ = ${35}^3$

So, $6,125\times \left(Y\right)=42,875$

$Y=\frac{42,875}{6,125}$

$Y=7$

Alternate solution,

By prime factorization of 6,125 , we get:
$6,125=5\times 5\times 5\times 7\times 7$

Hence,$\sqrt[3]{36,125\times \left(Y\right)}=35$
$\Rightarrow$ $\sqrt[3]{35\times 5\times 5\times 7\times 7\times \left(Y\right)}=35$

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

Given that cube root of 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.

$\sqrt[3]{36,125\times \left(Y\right)}=35$
$\Rightarrow$ $\sqrt[3]{35\times 5\times 5\times 7\times 7\times \left(Y\right)}=35$
$\Rightarrow$$\sqrt[3]{35\times 5\times 5\times 7\times 7\times \left(7\right)}=35$
$\Rightarrow$ $\sqrt[3]{36,125\times \left(7\right)}=35$

$\therefore Y=7$