Square Root of 960

The square root is the inverse of the square of the number. 960 is not a perfect square. The square root of 960 is expressed in both radical and exponential form. In the radical form, it is expressed as √960, whereas (960)^(1/2) in the exponential form. √960 = 30.98387, 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 960 is broken down into its prime factors.

Step 1: Finding the prime factors of 960 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 3 x 5: 2^5 x 3 x 5

Step 2: Now we found the prime factors of 960. The second step is to make pairs of those prime factors. Since 960 is not a perfect square, the digits of the number can’t be grouped in pairs that result in a perfect square.

Therefore, calculating 960 using prime factorization does not yield an exact integer.

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 960, we need to group it as 60 and 9.

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

Step 3: Now let us bring down 60, which is 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 ≤ 60; let us consider n as 0, now 6 x 0 x 0 = 0

Step 6: Subtract 60 from 0, the difference is 60, and the quotient is 30.

Step 7: Since the dividend is greater than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 6000.

Step 8: Now we need to find the new divisor that is 309 because 309 x 9 = 2781

Step 9: Subtracting 2781 from 6000, we get the result 3219.

Step 10: Now the quotient is 30.9

Step 11: Continue doing 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 √960 is approximately 30.98.

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 960 using the approximation method.

Step 1: Now we have to find the closest perfect square of √960. The smallest perfect square below 960 is 961, and the largest perfect square below 960 is 900. √960 falls somewhere between 30 and 31.

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 (960 - 900) ÷ (961-900) = 60/61 ≈ 0.98387 Using the formula, we identified the decimal point of our square root.

The next step is adding the value we got initially to the decimal number which is 30 + 0.98387 = 30.98387, so the square root of 960 is approximately 30.98387.

• Square root: A square root is the inverse of a square. 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.

• 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 the principal square root.

• Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors.

• Long division method: A method used to find the square root of a number by dividing the number into pairs and iteratively finding approximate values.