Square Root of 190
2026-02-21 20:43 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-190

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 190, we need to group it as 90 and 1.

Step 2: Now we need to find n whose square is less than or equal to 1. We can say n as ‘1’ because 1 × 1 is lesser than or equal to 1. Now the quotient is 1, and after subtracting 1 - 1 the remainder is 0.

Step 3: Now let us bring down 90, which is the new dividend. Add the old divisor with the same number 1 + 1 to get 2, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 2n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 2n × n ≤ 90. Let us consider n as 4, now 24 × 4 = 96, which is more than 90. Let us try n as 3, now 23 × 3 = 69.

Step 6: Subtract 90 from 69, the difference is 21, and the quotient is 13.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 2100.

Step 8: Now we need to find the new divisor, and the next number in the quotient. Let n be 8, then 278 × 8 = 2224.

Step 9: Subtracting 2224 from 2100 results in a negative number, which means 8 is too high. Let's try n as 7, now 277 × 7 = 1939.

Step 10: Subtracting 1939 from 2100 gives 161.

Step 11: Now the quotient so far is 13.7. Continue doing these steps until you get two numbers after the decimal point. Suppose if there are no decimal values continue till the remainder is zero.

So the square root of √190 is approximately 13.78.