Square Root of 1490
2026-02-28 09:06 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-1490

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 1490, we group it as 90 and 14.

Step 2: Now we need to find n whose square is 14. We can say n as ‘3’ because 3 x 3 is lesser than or equal to 14. Now the quotient is 3 and after subtracting 9 from 14, the remainder is 5.

Step 3: Now let us bring down 90 to make it the new dividend. Add the old divisor with the same number, 3 + 3, we get 6, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 6n x n ≤ 590. Let us consider n as 9, now 69 x 9 = 621, which is too large. So, try n = 8, 68 x 8 = 544.

Step 6: Subtract 544 from 590, the difference is 46, and the quotient is 38.

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 4600.

Step 8: Now we need to find the new divisor that is 386 because 3860 x 1 = 3860.

Step 9: Subtracting 3860 from 4600, we get the result 740.

Step 10: Now the quotient is 38.1

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

So the square root of √1490 is approximately 38.60.