Squaring Tricks
METHOD 1: Squaring a number ending with 5
We can very eaisly calculate the square of a number ending with 5.
Let n5 be a number where n is an integer.STEP 1: $ n \times (n+1)$ which gives the left hand side answer.
STEP 2: $ 5^{2}=25$ which gives the right hand side answer.
Combing the STEP 1 output and STEP 2 output we will get the final result.
In General,
$(n5)^2= \underparen { \quad n \times (n+1) \\ \text{LHS ANSWER}}$ $ \qquad \underparen {\qquad 25 \\ \text{RHS ANSWER}}$
Example 1: Find square of 35?
STEP 1: Here n=3, $3 \times (3+1) =12$
STEP 2: 25
STEP 3: Combining the STEP 1 and STEP 2 together we will get our final result i.e 1225
Example 2: Find square of 335?
STEP 1: Here n=33, $33 \times (33+1) =1122$
STEP 2: 25
STEP 3: Combining the STEP 1 and STEP 2 together we will get our final result i.e 11225
METHOD 2: Squaring a number ending with 5
By using four simple steps and we can find result.
STEP 1: Insert a separator before the 1's digit of the given number.
STEP 2: Multiply the first digit [i.e before the separator] with the next higher number which gives the LHS of the answer.
STEP 3: Square the 1's digit of the given number which gives the RHS of the answer.
STEP 4: Combining the LHS and RHS together then we will get the result.
Lets see some examples:
Example 1: Find out square of 35.
STEP 1: 3__5 [Here __ is used for separator.]
STEP 2: 3 X 4=12 [left side answer]
STEP 3: $(5)^2=25$ [right side answer]
STEP 4: Combining the left hand side and right hand side together we get our final result i.e 1225.
Example 1: Find out square of 335.
STEP 1: 33__5 [Here __ is used for separator.]
STEP 2: 33 X 34=1122 [left side answer]
STEP 3: $(5)^2=25$ [right side answer]
STEP 4: Combining the left hand side and right hand side together we get our final result i.e 11225.