Math tricks for squaring numbers

Squaring a two digit number

Algebra equation:

(AB) 2               [Here A is ten’s digit and B is one’s digit]

= (10A + B) 2

= (10A) 2 + 2 x 10A x B + B2

= 100A2 + 10 x 2AB + B2

So,

One's digit = B2

Ten's digit = 2 x A x B

Hundred's digit = A2

Algorithm:

Step 1.  Square the one’s digit (B). Write the one’s digit number from result, carry other digit. (B2)

Step 2.  Multiply the one’s (B) digit with the ten’s (A) digit and multiply by 2 then plus the carry (get from step 1). Write the one’s digit number from result, carry other digit. ((B*A)*2 + carry)

Step 3.  Square the ten’s digit (A) then plus carry (get from step 2). Write this result. (A2 + carry)

Examples:

Example 1.  432 =_________.

Step 1. 32

= 9

Write 9, carry 0.

Step 2. (3 x 4) x 2 + 0

= 12 x 2 + 0

= 24 + 0

= 24

Write 4, carry 2.

Step 3.  42 + 2

= 16 + 2

= 18

Write 18.

The answer is 1849.

Example 2.  672 =_________.

Step 1. 72

= 49

Write 9, carry 4.

Step 2. (7 x 6) x 2 + 4

= 42 x 2 + 4

= 84 + 4

= 88

Write 8, carry 8.

Step 3.  62 + 8

= 36 + 8

= 44

Write 44.

The answer is 4489.