Square Root of 4.2

The square root is the inverse of the square of the number. 4.2 is not a perfect square. The square root of 4.2 is expressed in both radical and exponential form. In the radical form, it is expressed as √4.2, whereas (4.2)^(1/2) in the exponential form. √4.2 ≈ 2.04939, 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 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 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 4.2, we need to consider it as 4.2.

Step 2: Now we need to find n whose square is closest to 4. We can say n is ‘2’ because 2 × 2 is equal to 4. Now the quotient is 2 after subtracting 4 from 4, the remainder is 0.

Step 3: Since we have a decimal, we bring down the next digit from the decimal part, which is 2, making the new dividend 20.

Step 4: Add the old divisor with the same number 2 + 2, we get 4, which will be our new divisor.

Step 5: The next step is finding 4n × n ≤ 20. Let's consider n as 0, now 4 × 0 × 0 = 0.

Step 6: Subtract 0 from 20, the difference is 20, and the quotient is 2.0.

Step 7: Since the dividend is larger than the divisor, we bring down another set of zeroes to continue the division process.

Step 8: Now we need to find the new divisor that fits the dividend. Repeat the steps to get more decimal places.

So the square root of √4.2 ≈ 2.04939.

The approximation method is another method for finding the square roots, and 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 4.2 using the approximation method.

Step 1: Now we have to find the closest perfect square of √4.2. The smallest perfect square less than 4.2 is 4, and the largest perfect square greater than 4.2 is 9. √4.2 falls somewhere between 2 and 3.

Step 2: Now we need to apply the formula that is: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Applying the formula: (4.2 - 4) / (9 - 4) = 0.2 / 5 = 0.04 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 2 + 0.04 ≈ 2.04, so the square root of 4.2 is approximately 2.04939.

• Square root: A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, that 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 the reason it is also known as the principal square root.

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

• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 4.2, 5.67, and 8.91 are decimals.