Square Root of 571

The square root is the inverse of the square of the number. 571 is not a perfect square. The square root of 571 is expressed in both radical and exponential forms. In radical form, it is expressed as √571, whereas in exponential form, it is (571)^(1/2). √571 ≈ 23.882, which is an irrational number because it cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0.

The prime factorization method is typically used for perfect square numbers. However, for non-perfect square numbers like 571, the long division method and approximation method are used. Let us now learn these 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 571 is broken down into its prime factors. Since 571 is a prime number, it cannot be factored further into smaller prime numbers. Therefore, calculating √571 using prime factorization is not applicable.

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 571, we need to group it as 71 and 5.

Step 2: Now we need to find n whose square is less than or equal to 5. We can say n is ‘2’ because 2^2 = 4, which is less than 5. Now the quotient is 2, and after subtracting 4 from 5, the remainder is 1.

Step 3: Now let us bring down 71, making the new dividend 171. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor.

Step 4: The new divisor becomes 4n. We need to find the value of n such that 4n × n ≤ 171. Let us consider n as 4, then 44 × 4 = 176, which is greater than 171. Therefore, n is 3, and 43 × 3 = 129.

Step 5: Subtract 129 from 171, the difference is 42, and the quotient is 23.

Step 6: 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 4200.

Step 7: The new divisor becomes 466, and we find that 466 × 8 = 3728.

Step 8: Subtracting 3728 from 4200, we get a remainder of 472.

Step 9: The quotient is now 23.8. Continue these steps until we get two decimal places.

So the square root of √571 ≈ 23.88.

The approximation method is another method for finding the square roots. It's an easy way to find the square root of a given number. Now let us learn how to find the square root of 571 using the approximation method.

Step 1: Now we have to find the closest perfect squares to √571. The smallest perfect square less than 571 is 529, and the largest perfect square greater than 571 is 576. Thus, √571 falls between 23 and 24.

Step 2: Now we need to apply the formula for approximation: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (571 - 529) / (576 - 529) = 42/47 ≈ 0.89. Adding this to the smaller square root, we get 23 + 0.89 = 23.89.

So the approximate square root of 571 is 23.89.

• Square root: The square root is the inverse operation of squaring a number. For example, if 5² = 25, then the square root of 25 is √25 = 5.

• Irrational number: An irrational number cannot be expressed as a simple fraction. It has a non-repeating, non-terminating decimal expansion, such as √571.

• Prime number: A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. For example, 571 is prime.

• Decimal: A decimal number contains a whole number and a fractional part separated by a decimal point, such as 23.88.

• Approximation: Approximation refers to finding a value close to the actual value. For example, √571 is approximately 23.88.