To
square numbers close to the base of multiples of 10, 100, 1000 and so on follow
the steps below:

Step-1: Find the surplus or deficit from the working base of multiples of 10, 100, 1000 and so on.Step-2: Add the surplus (if it is more than base) or subtract the deficit (if it is less than base) from the whole number given.Step-3: Multiply the result by the multiples of 10, 100, 1000 and so on the number is.Step-4: Find the square of surplus or deficit and write the result in the last places. Be sure that, for numbers multiples of 10; 1 more digit to go, since 10 has 1 zero, for numbers multiples of 100; 2 more digits to go, since 100 has 2 zeros, accordingly since 1000 has 3 zeros, 3 more digits to go for numbers multiples of 1000 and so on. So, carry forward or put extra zero(s) if necessary to place the digits accurate.

**408**

^{2}=?
Notice that 408 is close to 400 which
is 4 multiples of 100. So, our working base is 400 and actual base is 100.

1) Find the
surplus or deficit from base 400. It is (408–400=) 8 surpluses.

2) Since 408 is 8
more than base 400 so, add 8 to the given number, which is 408+8 = 416.

3) Now, since our working base 400 is 4 multiples of 100;
multiply 416 by 4 to get 1664. Write

**1664**as the first part of the answer.
4) Now, as the
actual base 100 has 2 zeros, so 2 more digits to go. Find the square of surplus
8 which is 64. Write

**64**as the last 2 digits of the answer.
So, our final answer is 166,464.

**588**

^{2}=?
Notice that 588 is close to 600 which
is 6 multiples of 100. So, our working base is 600 and actual base is 100.

1) Find the
surplus or deficit from base 600. It is (600–588=) 12 deficit.

2) Subtract 12
from the given number, which is (588-12=) 576.

3) Since working base 600 is 6 multiples of 100; multiply
576 by 6 to get the first part of the answer which is (576×6=) 3456.

4) Square of 12 is
144. Now, as the actual base 100 has 2 zeros, so 2 more digits to go. So, write
44 as the last 2 digits of the answer and carry 1 forwarded to 3456 to get
345744 as the final answer.

So, 588

^{2}= 345,744
Find

**67**^{2}
67 is (70 – 67=) 3 deficit from the base.

Since it is less than base, subtract the
deficit from the number i.e. 67 - 03 = 64.

Multiply this result by 7 since the base is
7 X 10 = 70.

64 x 7 = 448

Square of deficit = 3

^{2}= 9.
So the answer is 4,489.

**5015**

^{2}=?
Nearest base is 5000. Surplus = 15 and 5000
= 5 x 1000.

Since it is more than base, add the surplus
to the number to get (5015 + 15 =) 5030.

Multiply this result by 5 since base is 5 X
1000 = 5000.

5030 x 5 = 25150

Square of surplus = 15

^{2}= 225
So the final answer is 25,150,225 [since we
have taken multiples of 1000, write down 225 as it is].

**789**

^{2}=?
Actual Base is 100 and working Base is 800.

Deficit from working base is (800-789=) 11.

Subtracting the deficit from the number
gives (789-11=) 778.

Since 800 is 8 times 100, multiplying 778 by
8 gives (778X 8=) 6224.

Squaring the deficit gives (11

^{2}=) 121.
Since the base has 2 zeros, so place 21 and
carry forward 1 to 6224 to
get 6225.

So the final answer is 622,521.

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