find cube root by observation
Answers
Answer:
Cube roots of perfect cubes can be found out faster using Vedic Mathematics.
Points to remember
1. To calculate cube root of any perfect cube quickly, we need to remember the cubes of
1
to
10
(provided below).
1
3
=
1
2
3
=
8
3
3
=
27
4
3
=
64
5
3
=
125
6
3
=
216
7
3
=
343
8
3
=
512
9
3
=
729
10
3
=
1000
2. From the above cubes of
1
to
10
,
we need to remember an interesting property.
1
3
=
1
⇒
If last digit of perfect cube
=
1
,
last digit of cube root
=
1
2
3
=
8
⇒
If last digit of perfect cube
=
8
,
last digit of cube root
=
2
3
3
=
27
⇒
If last digit of perfect cube
=
7
,
last digit of cube root
=
3
4
3
=
64
⇒
If last digit of perfect cube
=
4
,
last digit of cube root
=
4
5
3
=
125
⇒
If last digit of perfect cube
=
5
,
last digit of cube root
=
5
6
3
=
216
⇒
If last digit of perfect cube
=
6
,
last digit of cube root
=
6
7
3
=
343
⇒
If last digit of perfect cube
=
3
,
last digit of cube root
=
7
8
3
=
512
⇒
If last digit of perfect cube
=
2
,
last digit of cube root
=
8
9
3
=
729
⇒
If last digit of perfect cube
=
9
,
last digit of cube root
=
9
10
3
=
1000
⇒
If last digit of perfect cube
=
0
,
last digit of cube root
=
0
It’s very easy to remember the relations given above as follows.
1
⟹
1
same numbers
8
⟹
2
10
's complement of
8
is
2
and
8
+
2
=
10
7
⟹
3
10
's complement of
7
is
3
and
7
+
3
=
10
4
⟹
4
same numbers
5
⟹
5
same numbers
6
⟹
6
same numbers
3
⟹
7
10
's complement of
3
is
7
and
3
+
7
=
10
2
⟹
8
10
's complement of
2
is
8
and
2
+
8
=
10
9
⟹
9
same numbers
0
⟹
0
same numbers
Also see
8
⟹
2
and
2
⟹
8
7
⟹
3
and
3
⟹
7
If we observe the properties of numbers, Mathematics is a very interesting subject and easy to learn. Now let’s see how we can actually find out cube roots of perfect cubes faster.
Example 1: Find Cube Root of 4913
Step 1
Identify the last three digits and make groups of three three digits from right side. i.e.,
4913
can be written as
4
,
913
Step 2
Take the last group which is
913.
The last digit of
913
is
3.
Remember point 2, If last digit of perfect cube
=
3
,
last digit of cube root
=
7
Hence the right most digit of the cube root
=
7
Step 3
Take the next group which is
4
Find out which maximum cube we can subtract from
4
such that the result
≥
0
We can subtract
1
3
=
1
from
4
because
4
−
1
=
3
(If we subtract
2
3
=
8
from
4
,
4
–
8
=
−
4
which is
<
0
)
Hence the left neighbor digit of the answer
=
1
i.e., answer
=
17
Example 2: Find Cube Root of 804357
Step 1
Identify the last three digits and make groups of three three digits from right side. i.e.,
804357
can be written as
804
,
357
Step 2
Take the last group which is
357.
The last digit of
357
is
7.
Remember point 2, If last digit of perfect cube
=
7
, last digit of cube root
=
3
Hence the right most digit of the cube root
=
3
Step 3
Take the next group which is
804
Find out which maximum cube we can subtract from
4
such that the result
≥
0
We can subtract
9
3
=
729
from
804
because
804
−
729
=
75
(If we subtract
10
3
=
1000
from
729
,
729
–
1000
=
−
271
which is
<
0
)
Hence the left neighbor digit of the answer
=
9
i.e., answer
=
93
Comments(68) Sign in (optional)
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Sarvajeet Suman 2 years ago
Find the cube root of
33076161
using this method ? Thanks in advance.
This comment is useful(0) This question is not useful(0) Reply
Javed Khan (Senior Math Expert, careerbless.com) 2 years ago
Grouping it gives
33076
,
161
Last digit of
161
is
1
. Therefore, last digit of the cube root is
1
33076
−
32
3
>
0
(Note that
33076
−
33
3
<
0
).
So, left side of the answer is
32
Answer is
321
For larger numbers, this method may not be that easy and to get the left side
32
, some calculations are involved. However, faster than the conventional way. If one can remember cubes of numbers up to
20
,
certainly more numbers can be covered easily.
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Nishant yadav 3 years ago
How to find cube root of a decimal number?
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Manoj (Alex) 3 years ago
How to find cube root more than 6 digit
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Anduna Abdul 3 years ago
this method is only applicable for finding cube root upto 6 digit numbers. But very nice though.
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chithiraivel 3 years ago
how to find a cube root of a simple number other than perfect cube?
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Raywant Bhatia 4 years ago
How to find cube root of 10 digit no.
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swarup 3 years ago
for that u need to know the cube of 10-20 or may be 20-30.
process is all same u have to solve unit digit rule as above then neglect last 3 digits and find the no whose cube value is nearest to remaining 7 digits.
if u cant then do again or reply back.
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Md.Arman 4 years ago
I have read all the process, it was very interesting but I may like to know how to find the cube root of a decimal and what if the cube root of the number is in decimal?