Show the full process to find the square root of 2 upto four decimal places.
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square root of 2= 1.4142
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this method,
Step 1: we place a dot and zeros (number of zero depends upon places upto which square root is to be found)
Step 2: make pairs and it is done in two steps (start from decimal and go right making pairs and then come back to decimal go right to left of decimal as shown).
Step 3: choose a number and square it such that it is less than or equal to 3 And then subtract it.
Step 4: add with itself(we add the number with the number was divided, in second part we can see we take 27.Here we multiplied 27*7 hence we add 7 to 27 and get 34). The divisor which in this case was 1 and hence we place 2 on the left as shown.
Step 5: As you see the dividend is 200(we bring the next pair after subtracting 3-1).
Step 6: As we can see we had added our divisor to 2 and we have 200 to divide. Sowe choose a number say "X" such that 2X*X is less just less than or equal to dividend.
Step 7: continue this process until desired (next time we double 27 and do 54X*X).

Therefore, √3 = 1.7324 ⇒ √3 = 1.73
1. the number 3.00003.0000 whose square root is to be calculated. We put the bar on the integral part of the number starting from the unit’s digit. This bar is placed in pairs. Similarly for decimal part, we put the bar on the pair of numbers starting from the digit which is immediately placed after the decimal. In this case it will be 3¯¯¯.00¯¯¯¯¯00¯¯¯¯¯3¯.00¯00¯
2. The divisor will be the maximum number whose square is less than or equal to the dividend that is the integral part of the number. In this case the divisor will be 1 and the dividend is 3. Divide and get the remainder.
3. The remainder in this case is22. Write the number which is in the next bar to the right side of the remainder. We get 200200.
4. Double the value of the divisor and enter it with a blank on its right. Since 0000 is the decimal part of the number, put a decimal point in the quotient.
5. Now we have to select the largest digit for the unit place of the divisor (22_) such that the new number when multiplied by the new digit at unit’s place is equal to or less than the dividend (200200). As we can see that27×7=18927×7=189, the new digit of the divisor is 77 and thus the divisor is 2727. Divide the number and get the remainder.
6. the remainder is 1111 and 0000 is left, therefore we get 11011000. Double the value of the divisor and enter it with a blank on its right. Now we have to select the largest digit for the unit place of the divisor (3434_) such that the new number when multiplied by the new digit at unit’s place is equal to or less than the dividend (11001100). As we can see that 343×3=1029343×3=1029.write 33 above.
we get the desired result3–√=1.733=1.73
Step 1: we place a dot and zeros (number of zero depends upon places upto which square root is to be found)
Step 2: make pairs and it is done in two steps (start from decimal and go right making pairs and then come back to decimal go right to left of decimal as shown).
Step 3: choose a number and square it such that it is less than or equal to 3 And then subtract it.
Step 4: add with itself(we add the number with the number was divided, in second part we can see we take 27.Here we multiplied 27*7 hence we add 7 to 27 and get 34). The divisor which in this case was 1 and hence we place 2 on the left as shown.
Step 5: As you see the dividend is 200(we bring the next pair after subtracting 3-1).
Step 6: As we can see we had added our divisor to 2 and we have 200 to divide. Sowe choose a number say "X" such that 2X*X is less just less than or equal to dividend.
Step 7: continue this process until desired (next time we double 27 and do 54X*X).

Therefore, √3 = 1.7324 ⇒ √3 = 1.73
1. the number 3.00003.0000 whose square root is to be calculated. We put the bar on the integral part of the number starting from the unit’s digit. This bar is placed in pairs. Similarly for decimal part, we put the bar on the pair of numbers starting from the digit which is immediately placed after the decimal. In this case it will be 3¯¯¯.00¯¯¯¯¯00¯¯¯¯¯3¯.00¯00¯
2. The divisor will be the maximum number whose square is less than or equal to the dividend that is the integral part of the number. In this case the divisor will be 1 and the dividend is 3. Divide and get the remainder.
3. The remainder in this case is22. Write the number which is in the next bar to the right side of the remainder. We get 200200.
4. Double the value of the divisor and enter it with a blank on its right. Since 0000 is the decimal part of the number, put a decimal point in the quotient.
5. Now we have to select the largest digit for the unit place of the divisor (22_) such that the new number when multiplied by the new digit at unit’s place is equal to or less than the dividend (200200). As we can see that27×7=18927×7=189, the new digit of the divisor is 77 and thus the divisor is 2727. Divide the number and get the remainder.
6. the remainder is 1111 and 0000 is left, therefore we get 11011000. Double the value of the divisor and enter it with a blank on its right. Now we have to select the largest digit for the unit place of the divisor (3434_) such that the new number when multiplied by the new digit at unit’s place is equal to or less than the dividend (11001100). As we can see that 343×3=1029343×3=1029.write 33 above.
we get the desired result3–√=1.733=1.73
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