Square Root of 5880

The square root is the inverse of the square of the number. 5880 is not a perfect square. The square root of 5880 is expressed in both radical and exponential form. In the radical form, it is expressed as √5880, whereas (5880)^(1/2) in the exponential form. √5880 ≈ 76.661, 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, for non-perfect square numbers, the long division method and approximation method are often used. Let us now learn the following methods:

• Prime factorization method
• Long division method
• Approximation method

The product of prime factors is the prime factorization of a number. Now, let us look at how 5880 is broken down into its prime factors.

Step 1: Finding the prime factors of 5880 Breaking it down, we get 2 x 2 x 2 x 3 x 5 x 7 x 7: 2^3 x 3 x 5 x 7^2

Step 2: Now that we have found out the prime factors of 5880, the second step is to make pairs of those prime factors. Since 5880 is not a perfect square, therefore the digits of the number can’t be grouped in pairs completely.

Therefore, calculating √5880 using prime factorization without approximation is not possible.

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 5880, we need to group it as 80 and 58.

Step 2: Now, we need to find n whose square is ≤ 58. We can say n = 7 because 7 x 7 = 49 is lesser than 58. Now the quotient is 7, and after subtracting 49 from 58, the remainder is 9.

Step 3: Now, let us bring down 80, which is the new dividend. Add the old divisor with the same number: 7 + 7 = 14, which will be our new divisor.

Step 4: The new divisor will be 14n. We need to find the value of n such that 14n x n ≤ 980. Let us consider n as 6; now 146 x 6 = 876.

Step 5: Subtract 876 from 980; the difference is 104, and the quotient is 76.

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 zeros to the dividend. Now, the new dividend is 10400.

Step 7: Now, we need to find the new divisor. Try n = 7; 1537 x 7 = 10759 (which is too large), so n = 6; 1536 x 6 = 9216.

Step 8: Subtracting 9216 from 10400, we get the result 1184.

Step 9: Now the quotient is 76.6

Step 10: 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 √5880 ≈ 76.66

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 5880 using the approximation method.

Step 1: Now, we have to find the closest perfect square of √5880.

The smallest perfect square less than 5880 is 5776, and the largest perfect square greater than 5880 is 5929. √5880 falls somewhere between 76 and 77.

Step 2: Now, we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula (5880 - 5776) / (5929 - 5776) = 0.65

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 76 + 0.65 = 76.65.

Therefore, the square root of 5880 is approximately 76.65.

• 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, 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 a principal square root.

• Prime factorization: This is the process of expressing a number as a product of its prime factors. For example, the prime factorization of 5880 is 2^3 x 3 x 5 x 7^2.

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