Question

What is the smallest number by which 17496 must be divided so that the quotient is a perfect cube

Answer 1

Answer:

3

Step-by-step explanation:

17496= 2×2×2. 3×3×3. 3×3×3. ×3

Here factor 3 is left therefore 17496 must be divided by 3 to obtain a perfect cube.

=17496/3

=5832

Cube root of 5832=18

Answer 2

Answer:

Given and Find:

• By what number should 17496 be divided to obtain a perfect cube.

Calculations:

• The number should be divided by the number 3.

⇢ 17,496 ÷ 3

⇢ 5,832

We know that = 17,496 = 3^7 × 2^3

That's,

⇢ 3^7 = (3 × 3 × 3 × 3 × 3 × 3 × 3 = 2187).

⇢ 2^3 = (2 × 2 × 2 = 8).

⇢ 3^7 × 2^3 = (2187 × 8)

⇢ 17,496

⇢ 3 × 3 × 2

⇢ 18