Square Root of 1352

The square root is the inverse of the square of the number. 1352 is not a perfect square. The square root of 1352 is expressed in both radical and exponential form. In the radical form, it is expressed as √1352, whereas 1352^(1/2) in the exponential form. √1352 ≈ 36.758, 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 and approximation methods 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 1352 is broken down into its prime factors.

Step 1: Finding the prime factors of 1352

Breaking it down, we get 2 x 2 x 2 x 13 x 13: 2^3 x 13^2

Step 2: Now we found out the prime factors of 1352. Since 1352 is not a perfect square, the digits of the number can’t be grouped in pairs completely. Therefore, calculating the square root of 1352 using prime factorization gives us √(2^3 x 13^2) = 2 x 13√2 = 26√2, which is approximately 36.758.

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 1352, we need to group it as 52 and 13.

Step 2: Now we need to find n whose square is less than or equal to 13. We can say n as '3' because 3 x 3 = 9, which is less than 13. Now the quotient is 3. After subtracting 9 from 13, the remainder is 4.

Step 3: Now let us bring down 52, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 6n as the new divisor; we need to find the value of n.

Step 5: The next step is finding 6n × n ≤ 452. Let us consider n as 7, now 67 x 7 = 469, which is too large, so we try n as 6.

Step 6: Now, 66 x 6 = 396. Subtracting 452 from 396, the difference is 56, and the quotient is 36.

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 5600.

Step 8: Now we need to find the new divisor that is 732 because 732 x 7 = 5124.

Step 9: Subtracting 5124 from 5600, we get the result 476.

Step 10: Now the quotient is 36.7

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

So the square root of √1352 is approximately 36.76.

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 1352 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1352. The smallest perfect square less than 1352 is 1296 (36^2), and the largest perfect square greater than 1352 is 1369 (37^2). √1352 falls somewhere between 36 and 37.

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 (1352 - 1296) ÷ (1369 - 1296) = 56 ÷ 73 ≈ 0.767 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 36 + 0.767 ≈ 36.767. So the square root of 1352 is approximately 36.767.

• 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 a 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.

• Divisor: A divisor is a number by which another number is to be divided.

• Approximation: The process of finding a value or quantity that is close to but not the exact number.