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## Square of 47, square of 215, Square Root of 5329, Cube of 37 and Cube Root of 59319 in JUST 10 SECONDS

**maths tricks and tips | www.aloksir.com | vedic maths | maths quiz | maths shortcut tricks | aalok srivastava **

** ****By ALOK SRIVASTAVA**

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**Rule 1.**

**(a) ****98 × 99 = 9702**

**Sol : 100 – 98 = 2**

**100 – 99 = 1**

**2 + 1 = 3**

**100 – 3 = 97**

**2 × 1 = 2**

**Since, Answer would be in 4 digits**

**so, 98 × 99 = 9702 .**

**(b) 94 × 93 = 8742**

**Sol:**

**100 – 94 = 6**

**100 – 93 = 7**

**94 – 7= 87, 93 – 6 = 87**

**So, we choose 87 once in answer**

**Now, 6 × 7 = 42**

**So, final answer would be 8742.**

**Rule 2**

**(a) 32 × 46 = 1472**

**Let A = 2 and B = 6 , C = 3 and D = 4****A × B****B × C + D × A****Add carry Numbers, if it is****C × D add carry numbers**

**See**

**2 × 6 = 12****Write 2 at once place and carry over is1.****6 × 3 + 4 × 2 = 26****Add 1. 26 + 1 = 27****Write 7 at ten’s place and carry over is 2****Then 3 × 4 = 12****12 + 2 = 14****Now we will have 1472**

**Three Digits Multiplication**

**Rule 1.**

**103 × 105 =**

**103 – 100 = 3****105 – 100 = 5****103 + 5 = 108, 105 + 3 = 108****We choose 108 once in answer****And 5 × 3 = 15****Final answer be 10815**

**Rule 2.**

**Any three digits Multiplication**

**472 × 389 =**

**Let A = 2 , B = 9, C = 8 , D = 7, E = 4 and F = 3****A × B****B × C + D × A****Add Carry numbers, if it is****B × E + F × A + C × D****Add carry over numbers, if it is****C × E + F × D, add carry numbers****E × F and add carry numbers****See,**

**2 × 9 = 18****Write 8 at one’s place and carry over is1****9 × 7 + 8 × 2 = 79****79 + 1 = 80****Write 0 at ten’s place and carry over is 8****9 × 4 + 3 × 2 + 8 × 7 = 98****98 + 8 = 106****Write 6 at hundred place and carry over is 10****8 × 4 + 3 × 7 = 53****53 + 10 = 63****Write 3 at thousand place and carry numbers is 6****4 × 3 = 12****Add 12 + 6 = 18****Now we will have 183608**

**Mixed Digits Multiplication**

**Rule 1**

**104 × 98 =**

**104 – 100 = 4****100 – 98 = 2****98 + 4 = 102, 104 – 2 = 102****So, we choose 102 once in answer****We will write 10200 first****Then subtract 4 × 2 = 8 from 10200****Now, we have 10200 – 8 = 10192**

**Rule 2**

**314 × 67 =**

**Let A = 3, B = 1, C = 4, D = 0, E = 6 and F = 7****C × F****B × F + E × C****F ×A + D × C + B × E****A × E + D × B****A × D****Now, we will have an answer**

**314 × 67**

**Let A = 3, B = 1, C = 4, D = 0, E = 6 and F = 7****4 × 7 = 28, take 8 as a unit place and carry over number is 2****1× 7 + 6 × 4 = 31****Add 2 to 31 means 2 + 31 = 33****Take 3 as a ten’s place and carry number is 3****7 × 3 + 0 × 4 + 1 × 6 = 27****27 + 3 = 30 (3 is carry number)****Take 0 as a thousand place and carry number is 3****3 × 6 + 0 × 1 = 18****18 + 3 = 21****Now answer would be 21038**

**Short cut to find Square of any Number**

** Square of any Two Digits**

**Square of 47**

**Square of 7 is 49****We will write 9 at unit place and carry over is 4****Then 4 × 7 × 2 = 56 and add 4 it becomes 60****Put 0 at ten’s place and carry over is 6****Square of 4 is 16 then add 6****16 + 6 = 22****Now we will have 2209**

**Square of 215**

**We will add 15 and subtract 15 for getting 200and 230****Square of 15 is 225****Choose 25 and carry over number is 2****Subtract 15 from 215, we will have 200 and adding 15 to 215, we will have 230****Then (200 × 230) ÷ 100 = 460****Add 460 + 2 ( 2 is carry over)= 462****Put 25 after 462****Now, we will have 46225**

**Square of 643**

**We will add 7 and subtract 7 for getting 650 and 636****Square of 7 is 49****Then (650 × 636) ÷ 100 = 4134****Put 49 after 4134****Now we will have 413449**

**Square Root of a Number**

**Square Root of √5329 =**

**Unit place digit can be 3 or 7****Focus first two digit 53****53 comes between 7**^{2}= 49 and 8^{2}= 64**So we will take small digit 7 at ten’s place****Now for unit digit, 7 and just after 8 we multiply 7 × 8 = 56****Since 53 is less than 56 so, unit place would be 3****Now answer would be 73.**

**Square root of 6724**

**Square of 2 is 4 and square of 8 is 64 so may be 2 or 8 at unit place**

**67 comes between 64 and 81 which is square of 8 and 9**

**Then focus 67 which is near by 64 and it is square of 8**

**Answer would be 82**

**Square Root of 47961**

**Unit place digit can be 1 or 9****Now, consider 479****Square of 22 is 484 which is greater than 479 so take square of 21 = 441****Take 21 in first place****Now talking about unit place****Here we multiply 21 × 22 = 462****Since 479 is greater than 462 so take 9 as a unit place****Now answer would be 219**

**Cube of Two Digits Number**

**(12)**^{3 }=**Let A = 1 and B = 2****Write A B B**^{2 }B^{3 }

**+ 2×B 2× B**^{2}

^{2}

** A B + 2 × B B**^{2} + 2 × B^{2} B^{3}

^{2}+ 2 × B

^{2}B

^{3}

**So, (12)**^{3} = 1 2 4 8

^{3}= 1 2 4 8

**+ 4 8**

** 1 7 2 8**

**Cube Root of a Number**

**Cube Root of √ 59319 =**

**We will take unit place digit 9 as it****Now focus first two digit 59****59 comes between 3**^{3 }= 27 and 4^{3}= 64**So we will take small digit 3 at ten’s place****Then answer would be 39**

**Cube Root of √157464 =**

**We will take unit place digit 4 as it****Now focus first three digit 157****157 comes between 5**^{3 }= 125 and 6^{3}= 216**So we will take small digit 5 at ten’s place****Then answer would be 54**

**Trick to Learn Table (2 to 100)**

**Here, I am not talking about table from 2 to 9 as it is very easy to learn.**

**Table of 12**

**See, we can take any table. So let’s talk about table of 12 first****Here 2 s one’s place and 1 is ten’s place****So when we talk about 12 × 7****Remember, we are not going to multiply 7 × 2 = 14 first****First of all, we will observe 12 as 10 + 2****Now we multiply 7 × 10 first and it becomes 70****And then 2 × 7 = 14****Now, 70 + 14 = 84.**

**Important Note: You can apply the same method on table of 12 to 99**

** Next example table of 74**

**Suppose 74 × 8 =****We can see 74 as 70 + 4****We will do 70 × 8 first****It becomes 560****Then we multiply 4 × 8 = 32****Now , 560 + 32 = 592**

**Digital Root Method**

**Digital Root means sum of all the digits should be equal to single digit. In this case, 9 is always equal to zero.**

**Example: 2567**

**Sum of this number 2 + 5 + 6 + 7 = 20**

**Again 2 + 0 = 2**

**Here we have single digit 2**

**So, this is a digital method.**

**Example 2053 +232 +1965 + 654 = ?**

**(a) 4904****(b) 3954****(c) 3636****(d) 2335**

**Solution : 2053 = 2 + 0 + 5 + 3**

**= 10**

**= 1+ 0**

**= 1**

**232 = 2 + 3 + 2**

**= 7**

**1965 = 1 + 9 + 6 + 5**

**1 + 0 + 11**

**= 12**

**1+ 2**

**= 3**

**654 = 6 + 5 + 4 = 6 + 9**

**6 + 0**

**= 6**

**Now total would be 1 + 7 + 3 + 6**

**= 1+ 7 + 9**

**= 8 + 0**

**= 8**

**CORRECT OPTION is (b) as 4904**

**= 4 + 9 + 0 + 4**

**= 4 + 0 + 0 + 4**

**= 8**

**Example : (86)**^{2 }= ?**(a)****( a) 6386****(b) 7396****(c) 8366****(d) 7346**

**Solution : (86)**^{2} = 86 × 86

^{2}= 86 × 86

**8 + 6 × 8 + 6**

**= 14 × 14**

**= 1 + 4 × 1 + 4**

**= 5 × 5**

**= 25**

**= 2 + 5**

**= 7**

**OPTION (b) is CORRECT as 7396**

**7 + 3 + 9 + 6**

**= 7 + 9 + 0**

**= 7 + 0 + 0**

**= 7**

**Division Trick Using Digital Sum**

**Important note: in digital case, 9 is always equal to 0 .**

**25 ÷ 2345 = ?**

**350****450****250****750**

**Let’s start**

**340025 = 2345 × X**

**3 + 4 +0 + 0 +2 + 5 = 2 + 3 + 4 + 5 × X**

**9 + 5 = 9 + 5 × X**

**0 + 5 = 0 + 5 × X**

**5 = 5 × X**

**Now X = 1**

**Now focus on Option (a)**

**350 = 1 + 3 + 5 + 0**

**= 9 + 0**

**= 0**

**450 = 1 + 4 + 5 + 0**

**= 1 + 9**

**= 1 + 0**

**= 1**

**So answer would be 1.450**

**Division By Short cut Method**

** (a) 478 / 5**

**= (478 × 2) / 5 × 2**

**= 956 / 10**

**= 95.6**

** (b) 232 / 25**

**= (232 × 4) / 25 × 4**

**= 928 / 100**

**= 9.28**

** (c) 118 / 125**

**= (118 × 8) / 125 × 8**

**= 944 /1000**

**= 0.944**

**Maths Magical Tricks**

**Value of √2 + √2 + √ 2 + √ 2 +………….Infinite**