Squaring a Number- Speed Maths www.competitionmentor.com

Square of no. ending with 5 A quick way to square numbers that end in 5 using the formula. BY ONE MORE THAN THE ONE BEFORE. 75^2 = 5625 75^2 means 75 x 75. The answer is in two parts: 56 and 25. The last part is always 25. The first part is the first number, 7, multiplied by the number “one more”, which is 8: so 7 x 8 = 56 www.competitionmentor.com

First figures are the same and the last figures add up to 10 Method for multiplying numbers where the first figures are the same and the last figures add up to 10. 32 x 38 = 1216 Both numbers here start with 3 and the last figures (2 and 8) add up to 10. So we just multiply 3 by 4 (the next number up) to get 12 for the first part of the answer. And we multiply the last figures: 2 x 8 = 16 to get the last part of the answer. www.competitionmentor.com

Squares of no from 26 to 75 There are lots of method– but i will discuss only one which is applicable to all & the easiest one. For numbers close to 50 i.e. for numbers from 30 to 75: Here we find the surplus (or deficit) of the number from 50, denoted by x in the following expression and then use the following to find the square. (50 + x)^2 = 25 + x | x^2 The answer is arrived at in two parts, separated by ‘|’ in the above expression. The right hand part of the answer has to be exactly two digits. Any extra digit has to be carried forwarded to the left hand part. And if the right hand part is a single digit, it has to be superseded with 0. E.g. 51^2 = (50 + 1)^2 = 25 + 1 | 1^2 = 26 | 01 = 2601 59^2 = (50 + 9)2 = 25 + 9 | 9^2 = 3481 www.competitionmentor.com

Numbers close to 100 i.e. for numbers from 75 to 130 Expression and then use the following to find the square. (100 + x)^2 = 100 + 2x | x^2 The answer is arrived at in two parts, separated by ‘|’ in the above expression. The right hand part of the answer has to be exactly two digits. Any extra digit has to be carried forwarded to the left hand part. And if the right hand part is a single digit, it has to be superseded with 0. E.g. 103^2 = (100 + 3)^2 = 100 + 2 x 3 | 3^2 = 106 | 09 = 10609108^2 = (100 + 8)^2 = 100 + 2 x 8 | 8^2 = 116 | 64 = 11664114^2 = (100 + 14)^2 = 128 | 196 = 12996 www.competitionmentor.com

Numbers close to 200 i.e. for numbers from 175 to 230 Expression and then use the following to find the square. (100 + x)^2 = (100 + 2x)*2 | x^2 The answer is arrived at in two parts, separated by ‘|’ in the above expression. The right hand part of the answer has to be exactly two digits. Any extra digit has to be carried forwarded to the left hand part. And if the right hand part is a single digit, it has to be superseded with 0. e.g. 203^2 = (200 + 3)^2 = (200 + 2 x 3)*2 | 32 = 412 | 09 = 41209 www.competitionmentor.com

Numbers close to 300 i.e. for numbers from 275 to 330: Expression and then use the following to find the square. (300 + x)^2 = (300 + 2x)*3 | x^2 The answer is arrived at in two parts, separated by ‘|’ in the above expression. The right hand part of the answer has to be exactly two digits. Any extra digit has to be carried forwarded to the left hand part. And if the right hand part is a single digit, it has to be superseded with 0. E.g. 303^2 = (300 + 3)^2 = (300 + 2 x 3 )*3| 3^2 = 918 | 09 = 91809 www.competitionmentor.com

For a base of 1000,2000,3000 & so on Last part must be 3 digit no. For a base of 10000,20000,30000 & so on— last part must be 4 digit no.; & so on. www.competitionmentor.com

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