Square Root of 6250

The square root is the inverse of squaring a number. 6250 is not a perfect square. The square root of 6250 is expressed in both radical and exponential forms. In radical form, it is expressed as √6250, whereas in exponential form, it is (6250)^(1/2). √6250 ≈ 79.05694, which is an irrational number because it cannot be expressed as a ratio of two integers.

The prime factorization method is used for perfect square numbers. For non-perfect square numbers like 6250, 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 6250 is broken down into its prime factors:

Step 1: Finding the prime factors of 6250. Breaking it down, we get 2 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 2 x 5^4 x 5^2.

Step 2: Now that we have found the prime factors of 6250, the second step is to form pairs of those prime factors. Since 6250 is not a perfect square, the digits of the number can’t be grouped into complete pairs, making it challenging to calculate the exact square root using prime factorization alone.

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, we need to group the numbers from right to left. In the case of 6250, we need to group it as 50 and 62.

Step 2: Identify the largest number whose square is less than or equal to 62. We can say this number is '7' because 7 x 7 = 49, which is less than 62. Now the quotient is 7, and after subtracting 49 from 62, the remainder is 13.

Step 3: Bring down the next pair of digits, which is 50, making the new dividend 1350. Add the old divisor to itself (7 + 7 = 14) to get the new divisor.

Step 4: Find a digit 'n' such that 14n x n is less than or equal to 1350. Let us consider n as 9, then 149 x 9 = 1341.

Step 5: Subtract 1341 from 1350; the difference is 9. The quotient now becomes 79.

Step 6: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend, making it 900.

Step 7: Continue the process to find the next digit. The new divisor is 158, and since 158 x 5 = 790, the next digit in the quotient is 5.

Step 8: Subtracting 790 from 900 gives 110. Continue this process until you achieve the desired precision.

So the square root of √6250 is approximately 79.056.

The approximation method is another method for finding square roots; it is a straightforward method to estimate the square root of a given number. Now let us learn how to find the square root of 6250 using the approximation method.

Step 1: Identify the closest perfect squares to √6250.

The smallest perfect square less than 6250 is 6084, and the largest perfect square greater than 6250 is 6400. Therefore, √6250 falls between 78 and 80.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula, (6250 - 6084) ÷ (6400 - 6084) ≈ 0.056. Add this decimal to the smaller integer root: 78 + 0.056 = 78.056.

Therefore, the square root of 6250 is approximately 79.056.

• Square root: A square root is the inverse of squaring a number. 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.

• Perfect square: A number that is the square of an integer. Example: 36 is a perfect square because it is 6^2.

• Decimal: If a number has both a whole number and a fractional part, it is called a decimal. Examples: 7.86, 8.65, and 9.42.

• Prime factorization: The expression of a number as a product of prime numbers. For example, the prime factorization of 50 is 2 x 5^2.