50 points
How to find root of any number like 2,3,5 by division method.
Answers
Taking 484 as the number whose square root is to be found. Place a bar over the pair of numbers starting from the unit’s digit. In case of an odd number the leftmost digit will also have a bar, 4¯¯¯ 84¯¯¯¯¯ .
Take the largest number as the divisor whose square is less than or equal to the number on the extreme left. The number on the extreme left is the dividend. Divide and write the quotient. Here the quotient is 2 and the remainder is 0.
We then bring down the number which is under the next bar to the right side of the remainder, in this case, we bring down 84. Now, 84 is our new dividend.
Now double the value of the quotient and enter it with a blank on the right side.
Now we have to select the largest digit for the unit place of the divisor (4_) such that the new number, when multiplied by the new digit at unit’s place, is equal to or less than the dividend (84).
The remainder is 0 and we have no number left for multiplication, Therefore,
Answer:
Step-by-step explanation:
We know that 2 can be written as 2.000000000000 i.e. 2=2.000000000000
see attachment 1
Now take a perfect square number which is below 2. We know that the perfect square number below 2 is 1.
see attachment 2
So write 1 in the divisor place and one more 1 in quotient place. Then subtract 1 from 2 the answer will be 1.
Next, carry down two zero’s and write after 1 and take the decimal point in quotient after 1.
see attachment 3
Now double the quotient and write in divisor place opposite to 100.after 2 we have to take a number and that same number we have to take in quotient also. Here I took 4 after 2 and the same number I wrote in quotient also after the decimal point. Now multiply like this 24 × 4 = 96. Then subtract 96 from 100 and write remainder as 4.
see attachment 4
Again carry down two zeros and write after 4, so now it becomes 400.
see attachment 5
Now opposite to 400 write 28 which is double the quotient 1.4 (don’t count. here take only number i.e. 14).
After 28 we take one number the same number we have to write in quotient after 4. Here I took one so that we can multiply like this 281 × 1 = 281 which is less than 400. Now do subtraction and write remainder i.e. here the remainder is 119.
see attachment 6
Next, carry down two zeros and write after 119, it becomes 11900.
see attachment 7
Now opposite to 11900 write 282 which is double the quotient 1.41 (don’t count. here take only number i.e. 141).After 282 we take one number the same number we have to write in quotient after 1. Here I took 4 so that we can multiply like this 2824 × 4 = 11296 which is less than 11900. Now do subtraction and write remainder i.e. here the remainder is 604.
see attachment 8
Next, carry down two zeros and write after 604, it becomes 60400.
see attachment 9
Now opposite to 60400 write 2828 which is double the quotient 1.414 (don’t count. here take only number i.e. 1414).
After 2828 we take one number the same number we have to write in quotient after 4. Here I took 2 so that we can multiply like this 28282 × 2 = 56564 which is less than 60400. Now do subtraction and write remainder i.e. here the remainder is 3836.
see attachment 10
Next, carry down two zeros and write after 3836, it becomes 383600.
square root of 2
Now opposite to 383600 write 28284 which is double the quotient 1.4142 (don’t count. here take only number i.e. 14142).
After 28284 we take one number the same number we have to write in quotient after 2. Here I took 1 so that we can multiply like this 282841 × 1 = 282841 which is less than 383600. Now do subtraction and write remainder i.e. here the remainder is 100759.
square root of 2
That’s it now we got the square root of 2 as 1.41421. we took root 2 value up to 5 decimal places. But in general square root of 2 value, it is enough to remember up to 3 decimal places i.e. root 2 value is 1.414.
