Square Root of 796

The square root is the inverse operation of squaring a number. 796 is not a perfect square. The square root of 796 is expressed in both radical and exponential form. In the radical form, it is expressed as √796, whereas in exponential form, it is (796)^(1/2). √796 ≈ 28.215, which is an irrational number as it cannot be expressed as a simple fraction.

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long division method and approximation method are used. Let us now learn these 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 796 is broken down into its prime factors.

Step 1: Finding the prime factors of 796 Breaking it down, we get 2 x 2 x 199. Since 199 is a prime number, 796 is expressed as 2² x 199.

Step 2: Now, we found out the prime factors of 796. Since 796 is not a perfect square, the digits of the number can’t be grouped into pairs, making it impossible to calculate the square root using prime factorization alone.

The long division method is particularly used for non-perfect square numbers. In this method, we try to find the closest perfect square number for the given number. Let us 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 796, we need to group it as 96 and 7.

Step 2: Now we need to find a number whose square is less than or equal to 7. We can take 2, as 2 x 2 = 4, which is less than 7. Now the quotient is 2. Subtracting 4 from 7 gives 3.

Step 3: Bring down 96 next to 3, making the new dividend 396. Double the previous quotient (2) to get 4, which will start our new divisor.

Step 4: Find a number, say n, such that 4n × n ≤ 396. We find n = 7 works because 47 x 7 = 329.

Step 5: Subtract 329 from 396 to get 67, and the quotient is now 27.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point, which allows us to add two zeroes to the dividend. The new dividend is 6700.

Step 7: Find the next digit n such that (540 + n) × n ≤ 6700. We find n = 1 works because 541 x 1 = 541.

Step 8: Subtract 541 from 6700 to get 6159, and the quotient is now 28.1.

Step 9: Continue this process until the desired precision after the decimal is achieved.

So the square root of √796 is approximately 28.215.

The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Let us learn how to find the square root of 796 using the approximation method.

Step 1: Find the closest perfect squares around 796.

The smallest perfect square less than 796 is 784 (which is 28²), and the largest perfect square greater than 796 is 841 (which is 29²). √796 falls between 28 and 29.

Step 2: Now apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) (796 - 784) / (841 - 784) = 12 / 57 ≈ 0.21

Add this to the base square root value of 28 to get approximately 28.21.

• Square root: A square root is the inverse of squaring a number. For example, 5² = 25, and the inverse is √25 = 5.

• Irrational number: An irrational number cannot be expressed as a simple fraction. For example, the square root of a non-perfect square is irrational.

• Radical form: A way to express roots, such as square roots, using the radical symbol (√).

• Exponential form: A mathematical notation indicating repeated multiplication, such as expressing roots as fractional exponents, e.g., x^(1/2).

• Perfect square: A number that is the square of an integer, such as 1, 4, 9, 16, etc.