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
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
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.