Square Root of 835

The square root is the inverse of the square of the number. 835 is not a perfect square. The square root of 835 is expressed in both radical and exponential form. In the radical form, it is expressed as √835, whereas (835)^(1/2) in the exponential form. √835 ≈ 28.9026, 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:

• 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 835 is broken down into its prime factors.

Step 1: Finding the prime factors of 835 Breaking it down, we get 5 x 167.

Step 2: Now we found out the prime factors of 835. Since 835 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating 835 using prime factorization alone does not yield a perfect square root.

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 835, we need to group it as 35 and 8.

Step 2: Now we need to find n whose square is less than or equal to 8. We can say n is ‘2’ because 2 x 2 = 4, which is less than 8. Now the quotient is 2, and after subtracting 4 from 8, the remainder is 4.

Step 3: Now let us bring down 35, which is the new dividend. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor in the form 4_.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we need to find n such that 4n x n ≤ 435. Let us consider n as 8, now 48 x 8 = 384.

Step 5: Subtract 384 from 435, the difference is 51, and the quotient is 28.

Step 6: 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 5100.

Step 7: Now we need to find the new divisor that fits into the dividend. Try 289 because 289 x 9 = 2601, which is less than 5100.

Step 8: Subtracting 2601 from 5100 we get the result 2499.

Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values continue till the remainder is zero.

So the square root of √835 is approximately 28.90.

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 835 using the approximation method.

Step 1: Now we have to find the closest perfect squares around √835.

The smallest perfect square less than 835 is 784 (which is 28^2), and the largest perfect square greater than 835 is 841 (which is 29^2). √835 falls somewhere between 28 and 29.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (835 - 784) / (841 - 784) = 51 / 57 ≈ 0.8947.

Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the integer part which is 28 + 0.8947 ≈ 28.895, so the square root of 835 is approximately 28.90.

• Square root: A square root is the inverse of a square. Example: 4^2 = 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.

• 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 why it is also known as the principal square root.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 28 is 2 x 2 x 7.

• Long division method: A method used to find the square root of non-perfect squares, involving a series of divisions and subtractions to achieve an approximate value.