Question

38^2-37^2

Is there any additional method, if there can you please show

Answer 1

I can tell you the general method.
38×38-37×37
=>1444-1369
=>75
Answer is 75.

There are some short cut methods. But it may be applicable for a short range or not good when number is large(depending upon the method used).
So i recommend you to do general method.

However, i will tell you a shortcut method for finding square.(Remember there are lots of short cut methods and this is only one of them)

Method:
This method uses the identity (a + b) ² = a ² + 2ab + b ²
Step 1 : Find 57²
Here a = 5 and b =7

Column I	Column II	Column III
a2	2 x a x b	b2
52= 25	2 x 5 x 7 =70	72= 49

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Step II: Underline the digit of b ² ( in column III) and add its tens digit, if any, to 2 x a x b (in column III)

Column I	Column II	Column III
a2	2 x a x b	b2
25	70 + 4 = 74	49

Step III: Underline the digit in column II and add the number formed by tens and other digit, if any, to a² in column I.

Column I	Column II	Column III
a2	2 x a x b	b2
25 + 7	70 + 4 = 74	49

Step IV: under the number in column I

Column I	Column II	Column III
a2	2 x a x b	b2
32	74	49

Write the underlined digits from the unit digit.
Therefore, 57 ² = 3,249 .

Hope it helps!