Basics of Cube & Roots - Free MCQ Practice Test with solutions, UPSC

0.064 = 64/1000= 4^3 / 10^3 =(4/10)^3= (2/5)^3 

taking cube root of 0.064= 2/5=0.4

Cube of multiple of 2 is divisible by 8
eg:

Prime factorise 3600.

You will get 3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5

Now group the numbers into groups of 3.

You will get 1 group of 2 and remaining numbers i.e. 2,3,3,5,5

Now multiply these extra numbers

You will get 2 x 3 x 3 x 5 x 5 = 450

So, 3600 divided by 450 = perfect cube (8)

Find prime factors of 5400

5400=2×3×3×3×2×2×5×5

If we group them in the group of 3

5400=(2×2×2)×(3×3×3)×5×5

Here to make group of 3 for 5

We have to multiply 5400 by 5.

The cube of an even natural number is always even. This can be understood through the following points:

• Even natural numbers can be expressed as 2n, where n is a natural number.
• When we cube an even number, we calculate (2n)³ = 8n³.
• Since 8n³ is a multiple of 2, it is therefore even.
• Thus, the cube of any even number will always yield an even result.

In summary, the conclusion is that the cube of all even natural numbers is even.

There'd no such digit which can't end in a cube of a natural number. Hence a cube of a natural number can end with any digit.
1³= 1 (ends with 1)
2³= 8 (ends with 8)
3³= 27 (ends with 7)
4³= 64 (ends with 4)
5³= 125 (ends with 5)
6³= 216 (ends with 6)
7³= 343 (ends with 3)
8³= 512 (ends with 2)
9³= 729 (ends with 9)
0³= 0 (ends with 0)
Hence the last digits are 0,1,8,7,4,5,6,3,2,9
Therefore we see every digits are last digits of these cubes. Hence a cube of a natural number can end with any digit.

0.2×0.2×0.2=0.008

Since, all the sides of the cube is painted, the cubes cut out from the corners will have three of its faces green. Since there are 8 corners for a cube, there will be 8 such cubes.