Square Root of 744

The square root is the inverse of the square of the number. 744 is not a perfect square. The square root of 744 is expressed in both radical and exponential form. In the radical form, it is expressed as √744, whereas in exponential form it is expressed as (744)^(1/2). √744 ≈ 27.284, 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 typically used for non-perfect square numbers, where the long-division method and approximation method are more suitable. Let us now learn about 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 744 is broken down into its prime factors: Step 1: Finding the prime factors of 744 Breaking it down, we get 2 × 2 × 2 × 3 × 31: 2^3 × 3 × 31 Step 2: Now we have found the prime factors of 744. The second step is to make pairs of those prime factors. Since 744 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √744 using prime factorization is not straightforward.

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 744, we need to group it as 44 and 7. Step 2: Now we need to find n whose square is less than or equal to 7. We can say n is ‘2’ because 2 × 2 = 4 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 44, which is the new dividend. Add the old divisor with the same number, 2 + 2, we get 4, which will be our new divisor. Step 4: The new divisor will be 4n. We need to find the value of n such that 4n × n is less than or equal to 344. Step 5: The next step is finding 4n × n ≤ 344. Let us consider n as 7, now 47 × 7 = 329. Step 6: Subtract 344 from 329; the difference is 15, and the quotient is 27. 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 1500. Step 8: Now we need to find the new divisor, which is 547 because 547 × 2 = 1094. Step 9: Subtracting 1094 from 1500, we get 406. Step 10: Now, the quotient is 27.2. Step 11: Continue doing these steps until we get two decimal places. If there is no decimal value, continue until the remainder is zero. So the square root of √744 is approximately 27.28.

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 744 using the approximation method. Step 1: Now we have to find the closest perfect squares of √744. The smallest perfect square below 744 is 729 (27^2) and the next largest perfect square is 784 (28^2). √744 falls somewhere between 27 and 28. 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 (744 - 729) / (784 - 729) = 15 / 55 ≈ 0.273. 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 27 + 0.273 ≈ 27.273, so the square root of 744 is approximately 27.28.

Square root: A square root is the inverse operation of squaring a number. Example: 4^2 = 16, and the inverse of the square is the square root, which is √16 = 4. Irrational number: An irrational number is a number that cannot be expressed as a fraction of two integers, where the denominator is not zero. Approximation method: A method of finding an approximate value of a number, often used when calculating the square root of non-perfect squares. Decimal: A number that consists of a whole number and a fractional part separated by a decimal point, for example, 7.86, 8.65, and 9.42. Long Division Method: A step-by-step division process used to find the square root of numbers that are not perfect squares.