Square Root of 79

The square root is the inverse of the square of the number. 79 is not a perfect square. The square root of 79 is expressed in both radical and exponential form.

In the radical form, it is expressed as √79, whereas (79)^(1/2) in the exponential form. √79 ≈ 8.888, 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 79 is broken down into its prime factors.

Step 1: Finding the prime factors of 79 79 is a prime number and can only be divided by 1 and 79 itself.

Step 2: Since 79 is not a perfect square, calculating √79 using prime factorization is not feasible.

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 79, we need to group it as 79.

Step 2: Now we need to find n whose square is less than or equal to 79. We can say n as ‘8’ because 8 × 8 = 64 is lesser than 79. Now the quotient is 8 after subtracting 64 from 79, the remainder is 15.

Step 3: Now let us bring down 00 to make it 1500, the new dividend. Add the old divisor with the same number 8 + 8 = 16, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 16n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 16n × n ≤ 1500. Let us consider n as 9, now 16 × 9 = 1449.

Step 6: Subtract 1449 from 1500, the difference is 51, and the quotient is 8.9.

Step 7: 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 √79 ≈ 8.88.

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 79 using the approximation method.

Step 1: Now we have to find the closest perfect square of √79. The smallest perfect square less than 79 is 64 (8^2), and the largest perfect square greater than 79 is 81 (9^2). √79 falls somewhere between 8 and 9.

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 (79 - 64) / (81-64) = 15 / 17 ≈ 0.882.

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 8 + 0.882 ≈ 8.882,

so the square root of 79 is approximately 8.882.

• 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, q is not equal to zero, and p and q are integers.

• Prime number: A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. Example: 2, 3, 5, 79.

• Long division method: A systematic method of dividing numbers to find the square root, especially useful for non-perfect squares.

• 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.