Question

what is the smallest number by which 8192 must be divided so that quotient is a perfect cube also find cube root of the quotient

Answer 1

Hello Dear!!!!

Here's your answer...

The given number is 8192

we have to do prime factorization

8192 - 2^13

8192 - 2^3 * 2^3 * 2^3 * 2^3 * 2^1

The power of 2 is 1

To become a perfect cube....The power should be 3

The power of remaining 2's is 3

But the power of one 2 is 1

So....it should be divided with 2

2 should be divided with 8192 to become perfect cube...

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HOPE THIS HELPS YOU....

Answer 2

Answer:

The smallest number by which 8192 must be divided so that quotient is a perfect cube is 2.

The cube root of quotient 4096 is 16.

Step-by-step explanation:

To find : What is the smallest number by which 8192 must be divided so that quotient is a perfect cube also find cube root of the quotient?

Solution :

The number 8192 factors are

$8192=2^{13}=(2\times2\times 2)^4\times 2$

i.e. 8192 make a perfect cube if we divide the number by 2 as 2 is an extra factor which doesn't make the cubic number.

So, The smallest number by which 8192 must be divided so that quotient is a perfect cube is 2.

Now, Dividing 8192 by 2 we get,

$\frac{8192}{2}=4096$

The quotient is 4096.

The cube root of 4096 is

$\sqrt[3]{4096}=16$

The cube root of quotient 4096 is 16.