Square Root of 956

The square root is the inverse of the square of the number. 956 is not a perfect square. The square root of 956 is expressed in both radical and exponential form. In the radical form, it is expressed as √956, whereas in exponential form it is expressed as (956)^(1/2). √956 ≈ 30.908, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

The prime factorization method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where long division method and approximation method are used. Let us now learn the following methods:

1. Prime factorization method
2. Long division method
3. Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 956 is broken down into its prime factors:

Step 1: Finding the prime factors of 956 Breaking it down, we get 2 x 2 x 239: 2² x 239¹

Step 2: Now we found out the prime factors of 956. The second step is to make pairs of those prime factors. Since 956 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating 956 using prime factorization is not straightforward.

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 956, we need to group it as 56 and 9.

Step 2: Now we need to find n whose square is less than or equal to 9. We can say n is ‘3’ because 3 x 3 = 9. Now the quotient is 3, and after subtracting 9 - 9, the remainder is 0.

Step 3: Now let us bring down 56, which is the new dividend. Add the old divisor with the same number 3 + 3 to 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 ≤ 56. Let us consider n as 8, now 68 x 8 = 544.

Step 6: Subtract 544 from 560, the difference is 16, 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 1600.

Step 8: Now we need to find the new divisor that is 617 because 617 x 2 = 1234.

Step 9: Subtracting 1234 from 1600, we get the result 366.

Step 10: Now the quotient is 30.9.

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

So the square root of √956 is approximately 30.908.

The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 956 using the approximation method.

Step 1: Now we have to find the closest perfect squares of √956. The smallest perfect square less than 956 is 900, and the largest perfect square more than 956 is 961. √956 falls somewhere between 30 and 31.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).

Going by the formula (956 - 900) ÷ (961 - 900) = 0.918. Adding this to the integer part of the square root, we get 30 + 0.918 = 30.918, so the square root of 956 is approximately 30.918.

• Square root: A square root is the inverse of a square. For example, 4^2 = 16 and the inverse of the square is the square root, that is √16 = 4.

• Irrational number: An irrational number is a number that cannot be written in the form of p/q, q is not equal to zero, and p and q are integers.

• Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root

• Factors: Factors are the numbers that divide a given number without leaving a remainder. For example, factors of 10 are 1, 2, 5, and 10.

• Long division method: A step-by-step method for finding the square root of a number by dividing the number into pairs of digits, starting from the decimal point.