Square Root of 713

The square root is the inverse of the square of a number. 713 is not a perfect square. The square root of 713 is expressed in both radical and exponential forms. In the radical form, it is expressed as √713, whereas, in the exponential form, it is expressed as (713)^(1/2). √713 = 26.698, 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:

• 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 713 is broken down into its prime factors.

Step 1: Finding the prime factors of 713 Breaking it down, we get 23 × 31.

Step 2: Now we found out the prime factors of 713. The second step is to make pairs of those prime factors. Since 713 is not a perfect square, we cannot group the digits of the number in pairs. Therefore, calculating 713 using prime factorization is impossible.

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 713, we need to group it as 13 and 7.

Step 2: Now we need to find n whose square is 7. We can say n is '2' because 2 × 2 is lesser than or equal to 7. Now the quotient is 2, and after subtracting 4 from 7, the remainder is 3.

Step 3: Now let us bring down 13, which is the new dividend. Add the old divisor with the same number, 2 + 2, to get 4, which will be our new divisor.

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

Step 5: The next step is finding 4n × n ≤ 313. Let us consider n as 6, now 46 × 6 = 276.

Step 6: Subtract 276 from 313, the difference is 37, and the quotient is 26.

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 3700.

Step 8: Now we need to find the new divisor that is 9 because 539 × 9 = 4851.

Step 9: Subtracting 4851 from 3700, we get the result -1151. Since 1151 is greater than zero, 26.9 is the next closest value.

Step 10: Now the quotient is 26.9.

Step 11: Continue performing these steps until we get two numbers after the decimal point.

So the square root of √713 is approximately 26.698.

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 713 using the approximation method.

Step 1: Now we have to find the closest perfect squares to √713. The smallest perfect square less than 713 is 676, and the largest perfect square greater than 713 is 729. √713 falls somewhere between 26 and 27.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula, (713 - 676) / (729 - 676) = 37 / 53 ≈ 0.698. 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 26 + 0.698 = 26.698, so the square root of 713 is approximately 26.698.

• 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: √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.

• Integers: The combination of whole numbers and negative numbers are integers. For example, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, etc., are integers.

• 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.