Square Root of 1088

The square root is the inverse of the square of the number. 1088 is not a perfect square. The square root of 1088 is expressed in both radical and exponential form. In the radical form, it is expressed as √1088, whereas (1088)^(1/2) in the exponential form. √1088 ≈ 32.9767, 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 1088 is broken down into its prime factors.

Step 1: Finding the prime factors of 1088 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 17: 2^5 x 17

Step 2: Now we found out the prime factors of 1088. The second step is to make pairs of those prime factors. Since 1088 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.

Therefore, calculating 1088 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 1088, we need to group it as 08 and 10.

Step 2: Now we need to find n whose square is closest to 10. We can say n is ‘3’ because 3 x 3 = 9 is lesser than or equal to 10. Now the quotient is 3, after subtracting 10 - 9, the remainder is 1.

Step 3: Now let us bring down 88, 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 6n. We need to find the value of n such that 6n x n is less than or equal to 188.

Step 5: The next step is finding 6n x n ≤ 188. Let us consider n as 3, now 63 x 3 = 189.

Step 6: Since 189 is greater than 188, we try n as 2: 62 x 2 = 124.

Step 7: Subtract 188 from 124. The difference is 64, and the quotient is 32.

Step 8: 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 6400.

Step 9: Now we need to find a new divisor that is 644. Consider n as 9: 644 x 9 = 5796.

Step 10: Subtracting 5796 from 6400, we get the result 604.

Step 11: The quotient becomes 32.9.

Step 12: Continue doing these steps until we get two numbers after the decimal point.

So the square root of √1088 is approximately 32.98.

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 1088 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1088. The smallest perfect square less than 1088 is 1024, and the largest perfect square greater than 1088 is 1156. √1088 falls somewhere between 32 and 34.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula (1088 - 1024) / (1156 - 1024) = 64/132 ≈ 0.4848 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 32 + 0.4848 ≈ 32.98.

So the square root of 1088 is approximately 32.98.

• 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, which 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 a principal square root.
   
• Long division method: A method used to find the square root of a number by dividing the number into groups of digits and performing division step by step.
   
• Approximation method: A technique used to estimate the square root of a number by identifying its position between two perfect squares and using an estimation formula.