Square Root of 79.93

The square root is the inverse of the square of a number. 79.93 is not a perfect square. The square root of 79.93 is expressed in both radical and exponential form.

In radical form, it is expressed as √79.93, whereas in exponential form it is (79.93)^(1/2). √79.93 ≈ 8.941, 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 like 79.93, the long division method and approximation method are used. Let us now learn the following methods

1.  Long division method
2. Approximation method

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, group the numbers from right to left. For 79.93, consider 79 and 93.

Step 2: Find n whose square is close to 79. We can say n as ‘8’ because 8 × 8 = 64, which is less than 79. Now, the quotient is 8. Subtract 64 from 79 to get the remainder of 15.

Step 3: Bring down the next pair of digits, 93, making it the new dividend of 1593. Add the old divisor with the same number, 8 + 8, to get 16, which will be our new divisor.

Step 4: The new divisor will be set as 16n. Find the value of n such that 16n × n ≤ 1593. Let us consider n as 9, now 169 × 9 = 1521.

Step 5: Subtract 1521 from 1593, leaving a difference of 72. The quotient is 8.9.

Step 6: Since the dividend is less than the divisor, add a decimal point and two zeroes to the dividend, making it 7200.

Step 7: Find the new divisor, 179, such that 179 × 4 = 7164.

Step 8: Subtract 7164 from 7200, yielding 36. Continue these steps until you achieve the desired precision.

The square root of √79.93 is approximately 8.94.

The approximation method is another method for finding square roots, and 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 79.93 using the approximation method.

Step 1: Find the closest perfect square to √79.93. The closest perfect squares are 64 and 81. √79.93 falls between these, so it is between 8 and 9.

Step 2: Apply the linear approximation formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square) (79.93 - 64) / (81 - 64) = 0.937

Using the formula, the result is 8 + 0.937 ≈ 8.937, so the square root of 79.93 is approximately 8.94.

• 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.

• Decimal: If a number has both a whole number and a fractional part, it is called a decimal, for example: 7.86, 8.65, and 9.42 are decimals.

• Long division method: A systematic method used to find the square root of non-perfect squares, involving dividing and finding successive approximations.

• Approximation method: A method to estimate the square root of a number by comparing it to nearby perfect squares and using linear interpolation.