Question

Find the square of the following numbers using column method. Verify the result by finding the square using the usual multiplication: 37

Answer 1

Hint: Here, for 37, let x = 3 and y = 7 and find its square using column method. And then find a square of 37 using the usual method i.e. by multiplying 37 × 37 and verify that both the results are the same.

Complete step-by-step answer:
We are given 37, in which the unit digit is 9 and tens digit is 3.
Here, x =3 and y =7
Step I: Make 3 columns and write the values of$x^2$,2xy and $y^2$ in these columns as below.

Column I	Column II	Column III
$x^2$	2xy	$y^2$
9	42	49

Step II: Underline the unit digit of $y^2$(in Column III ) and add its tens digit, with 2xy ( in column II)

Column I	Column II	Column III
$x^2$	2xy	$y^2$
9	42 + 4= 46	49

Step III: Underline the unit digit in Column II and add the number formed by the tens and other digits if any, with $x^2$ in Column I. Underline number in column I.

Column I	Column II	Column III
$x^2$	2xy	$y^2$
9 + 4= 13	42 + 4= 46	49

Step IV: Write all the underlined digits at the bottom of each column to get the square of the given number i.e. 37. Underlined digit in order are 13 6 7
So, we have:
${37}^2$=1369
Therefore, by column method we get ${37}^2$=1369
Now, using multiplication:
37 × 37=1369
We get the same result by both methods (Column method and usual method)

Note: Column method of finding square is method by which we can find square of number by writing numbers in particular structure and doing some simple calculation.