Let’s do this by examples

##
**
Find cube root of 857375.
**

**
Step 1:
**

Make group of 3 digit, starting from right

**
Step 2:
**

The unit digit of cube root will be

Unit digit of cube root of 857375 = Unit digit of cube root of 375.

Since 375 ends in 5, it’s cube root will end in 5.

(As
**
5
**
^{
3
}
= 12
**
5
**
, 1
**
5
**
^{
3
}
= 337
**
5
**
)

∴ Unit digit of cube root = 5

**
Step 3:
**

Now, for second group.

8 5 7

We note that

9
^{
3
}
= 729

& 10
^{
3
}
= 1000

So,

729 < 857 < 1000

9
^{
3
}
< 857 < 10
^{
3
}

∴ We take smaller number

So, 9

We put 9 in ten’s place of cube root

###
**
Find cube root of 658503.
**

**
Step 1:
**

Make group of 3 digit, starting from right

**
Step 2
**
**
:
**

The unit digit of cube root will be

Unit digit of cube root of 658503 = Unit digit of cube root of 503

Since 503 ends in 3, it’s cube root will end in 7.

(As
**
7
**
^{
3
}
= 34
**
3
**
, 1
__
7
__

^{ 3 }= 491

__)__

**3**

∴ Unit digit of cube root = 7

**
Step 3:
**

Now, for second group.

6 5 8

We note that

8
^{
3
}
= 512

& 9
^{
3
}
= 729

So,

512 < 658 < 729

8
^{
3
}
< 658 < 9
^{
3
}

∴ We take smaller number

So, 8

We put 8 in ten’s place of cube root.

∴ Cube root of 658503 = 87