Square Root of 480
2026-02-21 20:29 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-480

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 480, we need to group it as 80 and 4.

Step 2: Now we need to find n whose square is 4. We can say n as ‘2’ because 2 × 2 is lesser than or equal to 4. Now the quotient is 2, and after subtracting 4-4, the remainder is 0.

Step 3: Now let us bring down 80, which is the new dividend. Add the old divisor with the same number: 2 + 2, we get 4, which will be our new divisor.

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

Step 5: The next step is finding 4n × n ≤ 80. Let us consider n as 5, now 4 × 5 × 5 = 100, which is too large. Consider n as 4, now 4 × 4 × 4 = 64.

Step 6: Subtract 80 from 64, the difference is 16, and the quotient is 24.

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 1600.

Step 8: Now we need to find the new divisor. We use 48 because 484 × 4 = 1936, which is too large. So we use 47 because 474 × 3 = 1422.

Step 9: Subtracting 1422 from 1600 we get the result 178.

Step 10: Now the quotient is 21.9

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.

So the square root of √480 is approximately 21.91.