Square Root of 19.2
2026-02-28 08:48 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-19.2

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 19.2, we need to group it as 19 and 20 (19.2 is treated as 1920 for convenience).

Step 2: Now we need to find n whose square is the closest to the first group, which is 19. We can say n is '4' because 4^2 = 16, which is less than or equal to 19. Now the quotient is 4, and after subtracting 19 - 16, the remainder is 3.

Step 3: Bring down the next group, which is 20, to make it 320. Add the old divisor with the same number: 4 + 4 = 8, which will be our new divisor.

Step 4: The new divisor is 8n. Find n such that 8n × n ≤ 320. Let us consider n as 3, now 83 × 3 = 249.

Step 5: Subtract 320 from 249, the difference is 71, and the quotient is 4.3.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the remainder. Now the new dividend is 7100.

Step 7: Find the new divisor by considering 86 as the new divisor (83 + 3) and find n that satisfies 86n × n ≤ 7100. Suppose n is 8, then 868 × 8 = 6944.

Step 8: Subtract 6944 from 7100, we get the result 156.

Step 9: Continue doing these steps until we reach an appropriate level of precision.

So the square root of √19.2 is approximately 4.38178.