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.