Square Root of 967

The square root is the inverse of the square of the number. 967 is not a perfect square. The square root of 967 is expressed in both radical and exponential form. In the radical form, it is expressed as √967, whereas (967)^(1/2) in the exponential form. √967 ≈ 31.098, 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 the 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 967 is broken down into its prime factors:

Step 1: Finding the prime factors of 967 Since 967 is a prime number, it cannot be broken down further into prime factors.

Therefore, calculating 967 using prime factorization directly does not apply.

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 967, we group it as 67 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, which is less than or equal to 9. Now the quotient is 3, and after subtracting 9 from 9, the remainder is 0.

Step 3: Now let us bring down 67, 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, and we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 67. Let us consider n as 1, now 6 x 1 x 1 = 6.

Step 6: Subtract 6 from 67; the difference is 61, and the quotient is 31.

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 6100.

Step 8: Now we need to find the new divisor, which is 618 because 618 x 8 = 4944.

Step 9: Subtracting 4944 from 6100, we get the result 1156.

Step 10: Now the quotient is 31.09.

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

So the square root of √967 is approximately 31.10.

The approximation method is another method for finding the 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 967 using the approximation method.

Step 1: Now we have to find the closest perfect squares to √967. The smallest perfect square less than 967 is 961, and the largest perfect square greater than 967 is 1024. √967 falls somewhere between 31 and 32.

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

Going by the formula (967 - 961) ÷ (1024 - 961) = 0.095 Using the formula, we identified the decimal point of our square root.

The next step is adding the initial value we got to the decimal number, which is 31 + 0.098 = 31.098, so the square root of 967 is approximately 31.098.

• Square root: A square root is the inverse of a square. For example, 4² = 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, where q is not equal to zero and p and q are integers.

• Prime number: A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.

• Long division method: A method used to find the square root of non-perfect squares by dividing the number into groups and solving step by step to get an approximate value.