Question

7. Find the smallest number by which 8192 must be divided so that the quotient is a perfect square.

Also find the square root of the no. so obtained.​

Answer 1

Answer:

2

Explanation:

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.

Answer 2

$\huge{\underline{\mathfrak{Answer:-}}}$

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 28192=2

13

=(2×2×2)

4

×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

2

8192

=4096

The quotient is 4096.

The cube root of 4096 is

\sqrt[3]{4096}=16

3

4096

=16

The cube root of quotient 4096 is 16.