Know and learn the method or the process from which you can find the approximate value of the square root of 10. As the number 10 is not a perfect square, so we cannot get root 10 value easily.
If you want to know the square root of 10 value approximately (exact value difficult to find), we must use the long division method definitely.
We have to remember that there is no other method other than long division method to find the value of the square root of 10.
The Square root of 10 by long division method:
Now let’s see the process that should be followed for finding the value of root 10.
Draw the two vertical lines. In between vertical lines write the number 10. Write the number 10 as 10.000000…… after decimal point we can take as many as zeros because the value of 10 doesn’t change.
Now from left-hand side for every two digits keep the bar as shown in below diagram.
Now we have four groups. Take the first group i.e.10.
See that below 10 is there any perfect square. We have 9 as it can be written as 3 x 3. Write one 3 left-hand side and one 3 on right-hand side as shown in figure.
As 3 x 3 = 9 so write 9 below 10 and do subtraction 10 – 9 = 1 (remainder).
Carry down next group of digits i.e. 00 and write beside the remainder 1. Now it becomes 100.take the decimal point in the quotient after 3.
Right-hand side 3 i.e. quotient just double it and write opposite to 100.
3 double is 6. After 6 we should write one digit the same digit we have to write after 3. In the quotient.
I took 1 after 6 and 3. Then I multiplied 61 x 1 = 61.
Write 61 below 100 and subtract. 100-61 = 39 (remainder)
Carry next group of digits down and write beside 39. It becomes now 3900.
Now in quotient, we have 3.1 but consider 3.1 as 31 and double it and write opposite to 3900 left-hand side.
31 double is 62. After 62 we have to write one digit the same digit we have to write after 3.1 in the quotient.
I took 6 after 62 and after 3.1 in the quotient. Now multiply 626 x 6 = 3756. Write 3756 below 3900 and subtract.
The remainder is 144. Carry next group of digits down and write after 144 it becomes 14400.
Now double the quotient 3.16, forget about decimal point and take the only number i.e.316.
Double of 316 is 632. So write 632 opposite to 14400 on the left side.
After 632 take 2 and also in the quotient after 3.16 take 2 because if we take 3 the product of 6323 x 3 is more than 14400.
Write 12644 below 14400 and subtract it. The remainder is 1756.
Now we got the value of square root of 10 up to 3 decimal places. The value of the root 10 is 3.162.
If you want the value of root 10 up to 4 decimal places then you should continue the above process.
Below given are root 10 value up to 4, 5, 6, 7 and 8 decimal places:
The value of root 10 up to 4 decimal places is 3.1623
The value of root 10 up to 5 decimal places is 3.16227
The value of root 10 up to 6 decimal places is 3.162278
Root 10 value up to 7 decimal places is 3.1622778
Root 10 value up to 8 decimal places is 3.16227766