Question

Find the least natural number by which 2160 should be divided so that the quotient is a perfect cube . also find cube of quotient​

Answer 1

2160/2*5

2160/10

³√216=6

SO ANSWER IS 6//

Answer 2

The least natural number is 10, which after division leave 2160 as perfect cube number and $\bf \sqrt[3]{216} = 6$.

Step-by-step explanation:

Given:

• A number.
• $2160$

To find:

• Find the least natural number by which 2160 should be divided so that the quotient is a perfect cube .
• Also find cube root of quotient.

Solution:

Concept to be used:

• Do prime factorization of number.
• Make set of 3 same prime numbers.
• Take the numbers separately, which can not make pairs of three.

Step 1:

Do prime factorization of 2160.

$2160 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5$

Step 2:

Make pairs of 3 same prime factors.

$2160 = \underline {2 \times 2 \times 2} \times \underline{3 \times 3 \times 3} \times \red{2 \times 5}$

Step 3:

Find the least number for division.

As,

2 and 5 are separate from pairs.

Thus,

The least number is 10, by which 2160 is divided to get a perfect cube number.

Step 4:

Find the cube root of quotient.

On dividing 2160 with 10, we get 216 as quotient.

So,

$\sqrt[3]{216} = \sqrt[3]{ {2}^{3} \times {3}^{3} }$

or

$\sqrt[3]{216} = \sqrt[3]{ {(2 \times 3)}^{3} }$

or

$\sqrt[3]{216} = \sqrt[3]{ {6}^{3} }$

or

$\bf \sqrt[3]{216} = 6$

Thus,

The least natural number is 10, which after division leave 2160 as perfect cube number and cube root of 216 is 6.

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