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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:
What is the smallest number by which 3600 be divided to make it a perfect cube?
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)
Odd, Any odd number to power 3 will have unit digit odd
Ex. 7^3=3. 49^3=9.
(8.01)^{2} + ? = (8.97)^{2} What will approximately come in place of question mark?
The smallest number by which 5400 must be multiplied so that it become a perfect cube, is
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.
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
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