Name: Prime Factors of a Cube Number
Uploaded: 2019-07-19
Duration: 1 min 36 s
Description: The ages of four kids are prime numbers. If the product of their ages is 210, then how can we find their separate ages? Let's understand through this video.

Question

Find the smallest number that must be added to

400

to make it a perfect cube. Also find the cube root of this perfect cube.

Accepted Answer

The given number is $400$ .

In order to find the cube root of a perfect cube by successive subtraction method, subtract $1, 7, 19, 37, 61, . . . 1 + n \times (n - 1) \times 3$ , for $n = 1, 2, 3 . . .$ till the remainder is zero.

Thus, we can write

$400 - 1 = 399$

$399 - 7 = 392$

$392 - 19 = 373$

$373 - 37 = 336$

$336 - 61 = 275$

$275 - 91 = 184$

$184 - 127 = 57$

The next number to be subtracted from $57$ is $169$ .

But $169$ is greater than $57$

So, $169 - 57 = 112$ must be added to $400$ to make it perfect cube.

$∴ 400 + 112 = 512$ is a perfect cube.

Also, $\sqrt[3]{512} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$

Hence, $\sqrt[3]{512} = 2 \times 2 \times 2 = 8$

Find the smallest number that must be added to $400$ to make it a perfect cube. Also find the cube root of this perfect cube.

Important Questions on Cubes and Cube Roots

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