Squaring a number that ends in 50 is very easy.

This method can be applied to any number which is on either direction of 50, i.e. 55, 52, 47, …., 59 and so on.

There can be two cases:

**Case 1:****For numbers greater than 50**

*The result is comprised of two “parts”*

*The “right part” is always the right digit squared*

*The “left part” is the left digit squared plus the right digit.*

Let’s explore this with an example:

**54 ^{2}**

Here, the left digit is 5 and the right digit is 4.

So, the right part of the answer is square of the right digit, i.e. 4^{2}** = **16.

And, left part of the answer is square of left digit + right digit, i.e. 5^{2}+4 = 29

**54 ^{2} → **5

^{2}+4 / 4

^{2}

**29 / 16**

*→*

*→ 2916*Another example, 53^{2} ** → **25+3 / 9

**28 / 9**

*→*

*→ 2809***Case 2:****For numbers less than 50**

* **The result is comprised of two “parts”*

*The “right part” is always the bar of the right digit squared*

*The “left part” is the square of 5 minus **the bar of the right digit*

Let’s explore this with an example:

**48 ^{2}**

48 is near 50. The left digit is 4 and the right digit is 8.

So, the right part of the answer is the square of “bar of 8”.

Bar of 8 is 2.

Square of 2 is 2^{2}** = **4.

And, left part of the answer is square of 5, i.e. 5^{2}-2 = 23.

48^{2} ** → **5

^{2}-2 / (bar 8)

^{2 }

**25-2 / 2**

*→*^{2}

**23 / 04**

*→*

*→ 2304*Another example, 46^{2} ** → **25-4 / 4

^{2}

**21 / 16**

*→*

*→ 2116*