Η. Κ. Σ. Ι. Ε. Ζ. Ω. Φ. Cubes and Cube roots. Γ. Θ. Β. Α. θ. Δ. Contents. Introduction Perfect Cubes Cube root Cube root by prime factorisation Cube root by estimation. introduction.
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1729 = 1728+1=123 + 13
1729 = 1000+729=103 + 93
What is a cube
Numbers like 1, 8 ,27… are called cube numbers or a perfect cube . We get perfect cubes by multiplying a number
3 times with the same number.
THE SYMBOL “ ” DENOTES “CUBE ROOT ”
=33 × 53=(3×5)3
We find its cube root by prime factorisation.
The factors are ;
Therefore, cube root of 3375= 15
Find the cube root of 8000.
Prime factorisation of 8000 is
Therefore “ ” = 2×2×5=20
To find the cube root of a cube number, the following method can be used.
857375= 857 375
second number first number
We get 375 & 857 as two groups of three digits each
Take a cube number; 857375.
Make group of three digits starting from the right most digit of the number.
So,we get 5 at the unit’s place cube root.
We know that 9^3=729 & 10^3=1000.Also, 729<857<1000.We take the one”splace,place the as the ten “s place of the required cube root.So,we get “CR”857375=95
First group i.e.,375 will give the one’s digit of the required cube root.
The number 375 ends with 5.We know that 5 comes at the unit’s place of a number only when it’s cube root ends in 5.
Now we take the next group
WORK SHEET (FOR FA-3)
Find the cube root of each of the of the following by prime factorization method.
Find the cube root through estimation
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ANS – 128 IS NOT A PERFECT CUBE
ANS – NO IT’S NOT A PERFECT CUBE. IT SHOULD BE MULTIPLIED BY 5
ANS –NO IT’S NOT A PERFECT CUBE , IT SHOULD BE DIVIDED BY 44 TO GET A PERFECT CUBE.