Square Root of 529

The square root is the inverse of the square of the number. 529 is a perfect square. The square root of 529 is expressed in both radical and exponential form. In the radical form, it is expressed as √529, whereas (529)^(1/2) in the exponential form. √529 = 23, which is a rational number because it can 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. Since 529 is a perfect square, we can use the prime factorization method. Other methods such as the long division method or approximation method can also be used but are not necessary in this case.

1. Prime factorization method
2. Long division method
3. Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 529 is broken down into its prime factors.

Step 1: Finding the prime factors of 529 529 = 23 × 23 = 23²

Step 2: Since 529 is a perfect square, we can take one number from each pair of identical factors.

The square root of 529 is 23.

The long division method can also be used for perfect square numbers. It involves dividing the number into groups from right to left and finding the square root step by step.

Step 1: Group the digits of 529 from right to left as (5, 29).

Step 2: Find a number whose square is less than or equal to 5. The number is 2 because 2 × 2 = 4. Subtract 4 from 5, giving a remainder of 1. Bring down the next pair, 29, making it 129.

Step 3: Double the quotient (2) to get 4, which will be part of our new divisor.

Step 4: Find a digit (n) such that 4n × n ≤ 129. n is 3 because 43 × 3 = 129.

Step 5: Subtract 129 from 129 to get a remainder of 0. The quotient is 23, so the square root of 529 is 23.

Since 529 is a perfect square, the approximation method isn't necessary. However, for illustration:

Step 1: Identify two perfect squares between which 529 lies. Here, it is already a perfect square, i.e., 23² = 529.

Step 2: Since 529 is a perfect square, its square root is exactly 23.

Students sometimes make errors while finding the square root, such as forgetting about the negative square root or making calculation mistakes. Here are a few common mistakes and how to avoid them:

• Square root: A square root is the inverse of a square. Example: 23² = 529 and the inverse of the square is the square root, which is √529 = 23.

• Perfect square: A number that can be expressed as the product of an integer with itself.

• Rational number: A number that can be expressed in the form p/q, where p and q are integers and q ≠ 0.

• Prime factorization: The process of expressing a number as the product of its prime factors.

• Perimeter: The total distance around a two-dimensional shape, such as a square or rectangle.