Square root of 75
2026-02-28 17:39 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-75

This is a method used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.

Follow the steps to calculate the square root of 75:


Step 1 : Write the number 75, and draw a horizontal bar above the pair of digits from right to left.


Step 2 : Now, find the greatest number whose square is less than or equal to 75. Here, it is 8, Because 82=64 < 75.


Step 3 : Now divide 75 by 8 (the number we got from Step 2) such that we get 8 as quotient and then multiply the divisor with the quotient, we get 64. Subtract 64 from 75, we get 11. Add a decimal point after the quotient 8, and bring down two zeroes and place it beside 11 to make it 1100.


Step 4: Add 8 to same divisor, 8. We get 16.


Step 5: Now choose a number such that when placed at the end of 16, a 3-digit number will be formed. Multiply that particular number by the resultant number to get a number less than 1100. Here, that number is 6. 


166×6=996<1100.


Step 6: Do 1100-996=104. Again, bring down two zeroes and make 104 as 10400. Simultaneously add the unit’s place digit of 166, i.e., 6 with 166. We get here, 172. Apply Step 5 again and again until you reach 0. 

We will show two places of precision here, and so, we are left with the remainder, 4400 (refer to the picture), after some iterations and keeping the division till here, at this point 

              Step 7 : The quotient obtained is the square root. In this case, it is 8.660….