Square and Cube root

Square root

Example 1

Suppose we want to find the square root of 1225.

Step 1: Ignore last two digits of 1225. Remaining number left is ’12′.
Step 2: From the above table square of ’3′ is less than ’12′. Therefore left part (L) of our answer will be’3′.
Step 3: Since last digit of  ’1225‘ is ‘5‘. Therefore right part (R) of our answer will be ’5′.
Step 4: Our Answer will be L|R. Therefore Answer will be 3|5 = 35.

Therefore, √1225 = 35

Example 2

Suppose we want to find the square root of 5184.

Step 1: Ignore last two digits of 5184. Remaining number left is ’51′.
Step 2: From the above table square of ’7′ is less than ’51′. Therefore left part (L) of our answer will be’7′.
Step 3: Since last digit of  ’5184‘ is not equal to ’5′ or ’0′. Therefore right part (R) of our answer will not be be ’5′ or ’0′.
Step 4: Since last digit of 5184 is 4, Therefore right digit of answer will be either 2 or 8 (see table). Therefore, [L*(L+1)] = [7*(7+1)] = (7*8) = 56. since 56 is greater than 51, therefore right part of our answer will be 2.
Step 5: Our Answer will be L|R. Therefore Answer will be 7|2 = 72.

Therefore, √5184 = 72

 Example 3

Suppose we want to find the square root of 8649.

Step 1: Ignore last two digits of 8649. Remaining number left is ’86′.
Step 2: From the above table square of ’9′ is less than ’86′. Therefore left part (L) of our answer will be’9′.
Step 3: Since last digit of  ’8649‘ is not equal to ’5′ or ’0′. Therefore right part (R) of our answer will not be be ’5′ or ’0′.
Step 4: Since last digit of 8649 is 9, Therefore right digit of answer will be either 3 or 7 (see table). Therefore, [L*(L+1)] = [9*(9+1)] = (9*10) = 90. since 90 is greater than 86, therefore right part of our answer will be 3.
Step 5: Our Answer will be L|R. Therefore Answer will be 9|3 = 93.

Therefore, √8649 = 93

Ex -4

Square root of 15876

Step 1: Ignore last two digits of 15876. Remaining number left is ’158′.
Step 2: Square of ’12′ is less than ’158′. Therefore left part (L) of our answer will be’12′.
Step 3: Since last digit of ’15876‘ is not equal to ’5′ or ’0′. Therefore right part (R) of our answer will not be be ’5′ or ’0′.
Step 4: Since last digit of 15876 is 6, Therefore right digit of answer will be either 4 or 6 (see table). Therefore, [L*(L+1)] = [12*(12+1)] = (12*13) = 156. since 156 is less than 158, therefore right part of our answer will be 6.
Step 5: Our Answer will be L|R. Therefore Answer will be 12|6 = 126.

Therefore, √15876 = 126

Finding Squares

Ex 1. 43^2

step 1. Find base –no as 50-43=07

Step 2. Sq the no as 07^2=49.write it on the right side.

Step 3. Subtract the no from 25 as 25-7=18.write it on extreme left.

Step 4. Now this is Ur ans. 1849

Ex 2. 57^2

step 1. 57-50=7

Step2. 7^2=49

Step3. 25+7=32

step4. Ans is 3249.

Ex 3. 69^2

step1. 69-60=19 , 19^2=361

Step2. carry over 3 and write 61 in right side.

Step3 . 25+19=44, now add 44 with 3 (carry number) and write

it with extreme left.i.e. (25+19+3)

Step 4. ur ans is 4761

Ex4 . 38^2 step1. 50-38=12, 12^2=144, carry 1 and write 44 at right side .

Step2. now (25-12)+1=14 i.e. Carry number always adds (it never subtract). So ur ans is 1444.

So, 1. At first see the given no is it more or less than Ur base. If it is more then addition rule and if it be less, the n subtraction rule will be applied. That’s why (±) sign is given

2. And always add the carried no.

3. range is chosen making (±) 24 from base .

4. Trick is done by squaring the base excluding a 0 (zero) such for base 50:52=25.for base 350 , 35 2 = 1225

5. for(±) divide the base without zero by 5 as for base 100: 10/5=2,so trick is

100 (±)2(±) and for base 350: 35/5=7 ,and the trick is 1225(±)7(±) and so on.

Now we are giving more examples to clear the fact, a regular practice can make u

master of the art.ok, see

The following examples.

For base 100

Ex 5. 89^2

Step1. 100-89=11 ,11^2=121 ,carry 1

Step2. 100-(2 x 11 )+1=79, so the ans is 7921

Also u can use the alternative formula here,”given no (±)” such as

Step 1. 100-89=11,sq is 121,carry 1

Step2. 89-11+1=79 ,ass is 7921

(I think this process is better for numbers whose base is near 100)

Ex 6. 117²

Step1. 117-17=17, 17^2=289 ,carry 2

Step2. 117+17=134, 134+2=136 ,ans is 13689

For base 150

Ex 6. 139²

1. 150-139=11 , sq is 121 ,carry 1

2. 225-3×11=225-33=192, 192+1=193 ,ans is 19, 321

Ex 7. 164² 1. 164-150=14, 14²=196, carry 1

2. 225+3(14)=225+42=267 ,267+1=268 ,ans is 26,896

Ex 8. 512² 1. 12²=144 ,carry 1, 2500+10(12)+1=2621, ans is 26214

Cube root

Example 1

Suppose we want to find the cube root of 21952.

Step 1: Ignore last three digits of 21952. Remaining number left is ’21′.
Step 2: From the above table cube of ’2′ is less than ’21′. Therefore left part (L) of our answer will be ’2′.
Step 3: Since last digit of  ‘21952‘ is ‘2‘. Therefore right part (R) of our answer will be ’8′. (Because Last digit of ‘cube of 8′ is 2. see table above.)
Step 4: Our Answer will be L|R. Therefore Answer will be 2|8 = 28.

Example 2

Suppose we want to find the cube root of 148877.

Step 1: Ignore last three digits of 148877. Remaining number left is ’148′.
Step 2: From the above table cube of ’5′ is less than ’148′. Therefore left part (L) of our answer will be’5′.
Step 3: Since last digit of  ‘148877‘ is ‘7‘. Therefore right part (R) of our answer will be ’3′. (Because Last digit of ‘cube of 3′ is 7. see table above.)
Step 4: Our Answer will be L|R. Therefore Answer will be 5|3 = 53.

Example 3

Suppose we want to find the cube root of 636056.

Step 1: Ignore last three digits of 636056. Remaining number left is ’636′.
Step 2: From the above table cube of ’8′ is less than ’636′. Therefore left part (L) of our answer will be’8′.
Step 3: Since last digit of  ‘636056‘ is ‘6‘. Therefore right part (R) of our answer will be ’6′. (Because Last digit of ‘cube of 6′ is 6. see table above.)
Step 4: Our Answer will be L|R. Therefore Answer will be 8|6 = 86.

How to find the cube of a number

(ab)^3 = a^3 + 3a^2b + 3ab^2 + b^3