Question

Check weather 13824 is a perfect cube or not. If not, find the smallest number by which it should be multiplied to make it a perfect cube. Also, find the cube root of the perfect cube number so obtained.

Answer 1

yes, it is a perfect cube.

We can solve it by prime factorization method.

After resolving the prime factors, we get

13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

Grouping

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

Taking one factor from each group

∛13824 = 2 x 2 x 2 x 3

∛13824 = 24

Answer 2

13824 is a perfect cube

Solution:

Given that,

We have to check 13824 is a perfect cube or not

Find the prime factors and group together triplets of the prime factors

If no factor is left out then the number is a perfect cube

From given,

Find prime factors of 13824

The Prime Factorization is: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

Therefore,

$\sqrt[3]{13824} = \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 }\\\\Group\ into\ triplets\\\\\sqrt[3]{13824} = \sqrt[3]{2 \times 2 \times 2 } \times \sqrt[3]{2 \times 2 \times 2 } \times \sqrt[3]{2 \times 2 \times 2 } \times \sqrt[3]{3 \times 3 \times 3 }$

We know that,

$\sqrt[3]{2 \times 2 \times 2} = 2$

Therefore,

$\sqrt[3]{13824} = 2 \times 2 \times 2 \times 3\\\\ \sqrt[3]{13824} = 24$

Thus, 13824 is a perfect cube

Learn more about this topic

Using prime factorization method find 6859 is a perfect cube or not

https://brainly.in/question/6272046

216 is a perfect cube or not

https://brainly.in/question/5327572