Square root of 98
2026-02-28 10:26 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-98

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 98:


Step 1 : Write the number 98, 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 98. Here, it is 9, Because 92=81 < 98.


Step 3 : Now divide 98 by 9 such that we get 9 as quotient and then multiply the divisor with the quotient, we get 81. Subtract 81 from 98, we get 17. Add a decimal point after the quotient 9, and bring down two zeroes and place it beside 17 to make it 1700.


Step 4: Add 9 to same divisor, 9. We get 18.


Step 5: Now choose a number such that when placed at the end of 18, a 3-digit number will be formed. Multiply that particular number by the resultant number to get a number less than 1700. Here, that number is 8. 
188×8=1504<1700.


Step 6: Subtract 1700-1504=196. Again, bring down two zeroes and make 196 as 19600. Simultaneously add the unit’s place digit of 188, i.e., 8 with 188. We get here, 196. 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, 9799 (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 9.899….