Square Root of 1716

The square root is the inverse of the square of the number. 1716 is not a perfect square. The square root of 1716 is expressed in both radical and exponential form. In the radical form, it is expressed as √1716, whereas (1716)^(1/2) in the exponential form. √1716 ≈ 41.420, 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, the prime factorization method is not used; instead, 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 1716 is broken down into its prime factors.

Step 1: Finding the prime factors of 1716 Breaking it down, we get 2 x 2 x 3 x 11 x 13: 2^2 x 3 x 11 x 13

Step 2: Now we found out the prime factors of 1716. The second step is to make pairs of those prime factors. Since 1716 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating 1716 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 1716, we need to group it as 16 and 17.

Step 2: Now we need to find n whose square is closest to 17. We can say n as ‘4’ because 4 x 4 = 16 is lesser than or equal to 17. Now the quotient is 4 after subtracting 17 - 16 the remainder is 1.

Step 3: Now let us bring down 16 which is the new dividend. Add the old divisor with the same number: 4 + 4 = 8, which will be our new divisor.

Step 4: The new divisor will be 8n. We need to find the value of n.

Step 5: The next step is finding 8n × n ≤ 116. Let us consider n as 1, now 8 x 1 x 1 = 81.

Step 6: Subtract 116 from 81; the difference is 35, and the quotient is 41.

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 3500.

Step 8: Now we need to find the new divisor that is 82.5 because 825 x 4 = 3300.

Step 9: Subtracting 3300 from 3500 we get the result 200.

Step 10: Now the quotient is 41.4.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue till the remainder is zero.

So the square root of √1716 is approximately 41.42.

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 1716 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1716.

The smallest perfect square less than 1716 is 1600 and the largest perfect square greater than 1716 is 1764.

√1716 falls somewhere between 40 and 42.

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 (1716 - 1600) ÷ (1764 - 1600) = 116 / 164 ≈ 0.707.

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 40 + 0.707 = 40.707, so the square root of 1716 is approximately 41.42.

• 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 the reason it is also known as a principal square root.
   
• Prime factorization: Prime factorization is expressing a number as the product of its prime factors. For example, the prime factorization of 1716 is 2^2 x 3 x 11 x 13.
   
• Long division method: The long division method is used to find the square root of numbers that are not perfect squares by dividing the number into smaller parts and finding the square root step by step.