Square Root of 295
2026-02-28 01:13 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-295

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 295, we need to group it as 95 and 2.

Step 2: Now we need to find n whose square is 2. We can say n is ‘1’ because 1 x 1 is less than or equal to 2. Now the quotient is 1, after subtracting 1 from 2, the remainder is 1.

Step 3: Now let us bring down 95, which is the new dividend. Add the old divisor with the same number: 1 + 1, we get 2, which will be our new divisor.

Step 4: The new divisor will be 2n. We need to find the value of n such that 2n x n ≤ 195. Let us consider n as 7, now 27 x 7 = 189.

Step 5: Subtract 189 from 195, the difference is 6, and the quotient is 17.

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 zeroes to the dividend. Now the new dividend is 600.

Step 7: Now we need to find the new divisor that is 173 because 173 x 3 = 519.

Step 8: Subtracting 519 from 600, we get the result 81.

Step 9: Now the quotient is 17.3.

Step 10: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.

So the square root of √295 is approximately 17.17.