Square Root of 4900

The square root is the inverse of squaring a number. 4900 is a perfect square. The square root of 4900 can be expressed in both radical and exponential forms. In radical form, it is expressed as √4900, whereas in exponential form it is (4900)^(1/2). √4900 = 70, which is a rational number because it can be expressed in the form of p/q, where p and q are integers with q ≠ 0.

For perfect square numbers like 4900, the prime factorization method is often used. We can also use the long division method and approximation method, though they are more common for non-perfect squares. Let us explore these methods:

• Prime factorization method
• Long division method
• Approximation method

The product of prime factors is the prime factorization of a number. Let us break down 4900 into its prime factors:

Step 1: Finding the prime factors of 4900

Breaking it down, we get 2 × 2 × 5 × 5 × 7 × 7: 2^2 × 5^2 × 7^2

Step 2: Now that we have found the prime factors of 4900, we make pairs of those prime factors. Since 4900 is a perfect square, the digits of the number can be grouped in pairs. Therefore, the square root of 4900 using prime factorization is possible. Thus, √4900 = √(2^2 × 5^2 × 7^2) = 2 × 5 × 7 = 70.

The long division method can also be used for finding the square root of perfect square numbers. Let us learn how to find the square root using the long division method, step by step:

Step 1: To begin, we need to group the numbers from right to left in pairs. In the case of 4900, we group it as 49 and 00.

Step 2: Now we find a number whose square is less than or equal to 49. The number is 7 because 7 × 7 = 49. The quotient is 7, and the remainder is 0.

Step 3: Now, bring down the next pair of zeros, making it 00.

Step 4: Add the old divisor with the same number, 7 + 7 = 14, which will be our new divisor.

Step 5: Determine a number n such that 14n × n is less than or equal to 00. Here n is 0, because 140 × 0 = 0.

Step 6: Subtracting gives us 0 as the remainder.

Step 7: The quotient is 70, which is the square root of 4900.

The approximation method is straightforward for finding square roots. Let us learn how to find the square root of 4900 using this method:

Step 1: Find the closest perfect squares to √4900. The closest perfect squares are 4900 itself (exact) and no need for approximation.

Step 2: √4900 = 70 since it is a perfect square.

• Square Root: A square root is the value that, when multiplied by itself, gives the original number. Example: 70 × 70 = 4900, so √4900 = 70.

• Perfect Square: A number that is the square of an integer. 4900 is a perfect square because it equals 70^2.

• Rational Number: A number that can be expressed as the quotient or fraction p/q of two integers, where q is not zero. 70 is a rational number.

• Factorization: The process of breaking down a number into its prime components. For example, the prime factorization of 4900 is 2^2 × 5^2 × 7^2.

• Perimeter: The total distance around a two-dimensional shape. For example, the perimeter of a rectangle is calculated as 2 × (length + width).