CUBE
ROOT
#1.
REMEMBERING UNITS DIGITS : First we need to remember cubes
of 1 to 10 and unit digits of these cubes. The figure below shows the unit
digits of cubes (on the right) of numbers from 1 to 10 (on the left).
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Numbers
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Digits of Cube
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1
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1
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2
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8
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3
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7
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4
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4
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5
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5
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6
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6
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7
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3
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8
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2
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9
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9
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10
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0
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Now look at the image above. We can definitely say that: Whenever unit digit of a number is 9, the unit digit of the cube of that number will also be 9. Similarly, if the unit digit of a number is 9, the unit digit of the cube root of that number will also be 9. Similarly, if unit digit of a number is 2, unit digit of the cube of that number will be 8 and vice versa if unit digit of a number is 8, unit digit of the cube root of that number will be 2. Similarly, it will be applied to unit digits of other numbers as well.
#2.
DERIVING CUBE ROOT FROM REMAINING DIGITS: Let’s see this with the help of an example.
Note that this method works only if the number given is a perfect cube. Q. Find
the cube root of 474552. Unit digit of 474552 is 2. So we can say that unit
digit of its cube root will be 8. Now we find cube root of 474552 by deriving
from remaining digits. Let us consider the remaining digits leaving the last 3
digits. i.e. 474. Since 474 comes in between cubes of 7 and 8. So the ten’s
digit of the cube root will definitely be 7 i.e. cube root of 474552 will be
78. Let us take another example.
Q. Find the cube root of 250047. Since the
unit digit of the number is 7, so unit digit in the cube root will be 3. Now we
will consider 250. Since, 63 < 250 < 73 , So tens digit will be 6 So we
find cube root of the number to be 63. Here are some more examples.
Q. Simplify: ?970299 = ?
Unit digit of number is 9 ? Unit digit of cube root will be 9 Now we will
consider 970 Since, 93 < 970 < 103 So, we find cube root of the number to
be 99. Let’s take another example to make this trick clearer to you.
Q. Simplify: ?140608 = ? Unit digit of number
is 8 ? Unit digit of cube root will be 2 Now we will consider 140 Since, 53
< 140 < 63 So, we find cube root of the number to be 52.→→
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