MATH SHORT TRICKS

**Tip-1 ****How to find Square of a number ending with 5?**

**After learning this you will be able to find square of a nnumber ending with 5 say 25, 35, 45 etc. You can even try to find square of a three digit number ending with 5 say**

**105, 115, 125 etc.**

**Say you want to find square of 85**

**Do the following:**

• **Multiply 5 by 5 and put 25 as your right part of the answer.**

• **Multiply 8 by the next higher digit i.e 9 and put 72 as your left part of the answer.**

• **Your answer is 7225 .You can use this formula to find square of any number ending with 5.**

**Tip-2 ****How to find out square of an adjacent number?**

**You know the squares of 30, 40, 50, 60 etc. but if you are required to calculate square of 31 or say 61 then you will scribble on paper and try to answer the question.**

**Can it be done mentally?**

**Some of you will say may be and some of you will say may not be. But if I give you a formula then all of you will say, yes! it can be. What is that formula**

**…..**

**The formula is simple and the application is simpler.**

**Say you know 60 ^{2} **

**= 3600**

**Then 61**^{2} **will be given by the following**

**61**^{2} **= 60**^{2} **+ (60+61) = 3600 + 121 = 3721**

**or Say you know 25**^{2} **= 625 then**

**26**^{2} **= 625+ (25+26) = 676**

**Like above, you can find out square of a number that is one less than the number whose square is known.**

**Let me show it by taking an example: Say you know 60 ^{2} **

**= 3600**

**Then 59**^{2} **will be given by the following**

**59**^{2} **= 60**^{2} **- (60+59) = 3600 - 119 = 3481**

**or Say you know 25**^{2} **= 625 then**

**24**^{2} **= 625- (25+24) = 576**

**Apply it to find square of a digit, which is one, less than the square of a known digit. This works very well for the complete range of numbers.**

**Tip-3****How to find out square of a number near 100?**

**Numbers Less than 100**

**Say you want to find Square of 98.**

**98 is 2 away from 100. So what?**

**The square will be given by 98-2/02**^{2} **= 9604**

**Say you want to find Square of 97**

**97 is 3 away from 100.**

**Square of this will be given by 97-3/03**^{2} **= 9409**

**Numbers More than 100.**

**Say you want to find square of 102**

**102 is 2 away from 100, its 2 more than 100 therefore we will add 2 more to it and the square will be given by**

**102+2/ 02**^{2} **= 10404**

**After going through these three examples you should be able to understand the technique. The technique is to reduce or add as much as it is away from 100 and put square of difference on it.**

**Tip-4 ****Multiplication**

**The First Formula**

**To Multiply two digit numbers:**

**Remember:**

**1. The digits on the left hand should be same.**

**2. On adding the right hand digits you must get 10.**

**Example:**

**65 x 65 or 36 x 34**

**The Magical Method:**

**65 x 65 = 4225**

**What did we do?**

**1. We first multiplied the right hand side digits (5 x 5)**

**and wrote 25.**

**2. We added 1 to the left digit 6 and got 7.**

**3. We then multiplied 6 by 7 and wrote the answer 42 to**

**the left of 25.**

**4. We thus arrived at the answer 4225.**

**Let's try another example:**

**46 x 44**

**1. 6 x 4 = 24**

**2. 4 + 1 = 5**

**3. 4 x 5 = 20**

**4. Answer: 2024**

**Note:**

**What if we have to multiply 69 x 61?**

**The answer would be 4209.**

**But why the extra 0?**

**Because the right hand side of the answer should always have two digits.**

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