Column method for squaring a two digit number

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There are following steps to find the square a two digit number:-

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Let the given number have the tens digit = a and  the units digit = b

Then, we have to square this number.

Step 1 . Make three Columns, I II and III, headed by a^2, (2 x a x b) and b^2 respectively Write the vales of a^2, (2 x a x b) and b^2 in columns I, II and III respectively.

Step 2. In Column III, underline the units digit of b^2 and carry over the tens digit of it to Column II and add it to the value of (2 x a x b)

Step 3. In Column II, underline the unit digit of the number obtained in Step 2 and carry over tens digit of it to Column I and add it to the value of a^2.

Step 4. Underline the number obtained in Step 3 in Column I.

The underlined digits give the required square number.

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Example: Find the square of 47

Solution: Given number = 47

So a=4 and b=7

I	II	III
a^2	2ab	b^2
16 +6 22	56 +4 60	49

Hence the square of 47 = 2209