Vedic / Quicker / Shortcut Math ⇒ Topic : Square root a number ending with 5

Peter
 
Squaring a number ending in 5 is the easiest if you know the trick. Number given to you can be a two digit number or three digit number or five or six digit number, it does'n t matter. The same trick can be applied to find the square of any number ending in 5. Let us now discuss the steps to follow Step 1:Multiply the ten's digit of the given number with its immediate next number.This will be the 1st digit of the answer. Step 2:Put 25 next to the result of step 1. Logic behind putting 25 is that the number will always end with 5 and 5^{2} is 25. You get the answer Let us find squares of numbers ending in 5 using this trick Example 1:(35)^{2}=?Step 1: 3 is the ten's digit in the given number 35.Immediate next number to 3 is 4. Hence,by multiplying 3 & 4 we get 12(3x4=12).which is the 1st digit of the answer. Step 2: Now putting 25 next to 12 we get the answer as 1225. Answer: (35)^{2}= 1225 Now you try to square 25,45,15,55,65,75,85,95 & see how quickly you can square. Example 2:(125)^{2}=? Step 1: 12 is the ten's digit in the given number 125. Immediate next number to 12 is 13. Hence,by multiplying 12 & 13 we get 156(12x13=156).which is the 1st digit of the answer. [To multiply a 2digit by 2digit number when ten's digit of both numbers is 1 you can apply a trick to get your answer quickly. 1st digit =1 middle digit =add unit's place digit of both numbers(2+3=5) unit's place digit=Multiply unit place digit of both numbers(2x3=6)] Step 2: Now putting 25 next to 156 we get the answer as 15625. Ans (125)^{2}= 15625 Now you try to square 105,115,135,145,155,165,175,185,195 & see how quickly you can square.  
 
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