Square Root of 2/5

The square root is the inverse of the square of a number. The fraction 2/5 is not a perfect square. The square root of 2/5 can be expressed in both radical and exponential form. In radical form, it is expressed as √(2/5), whereas (2/5)^(1/2) in exponential form. The square root of 2/5 is approximately 0.632455, which is an irrational number because it cannot be expressed as a ratio of two integers.

The prime factorization method is not applicable to non-integers. For fractions, we can find the square root by finding the square root of the numerator and the denominator separately. Let us now learn the following methods: Simplifying the fraction Finding square roots of numerator and denominator

To simplify the process, let's understand how to handle the square root of a fraction. If we have √(a/b), we can separate this into √a/√b. Now, let's apply this to 2/5.

Step 1: Separate the fraction as √2/√5

Step 2: Calculate the square root of the numerator and the denominator. √2 ≈ 1.414 and √5 ≈ 2.236

Step 3: Divide the square root of the numerator by the square root of the denominator. So √(2/5) ≈ 1.414/2.236 ≈ 0.632455

Therefore, the square root of 2/5 is approximately 0.632455.

The long division method is a systematic way to find the square root of non-perfect square numbers, including decimals. Let's see how to find the square root using this method, step by step.

Step 1: Convert 2/5 into a decimal, which is 0.4.

Step 2: Use the long division method to find the square root of 0.4.

Step 3: Pair the digits of 0.4 from the decimal point, so we have 40.

Step 4: Find a number whose square is less than or equal to 40. Let's take 6, as 6*6 = 36.

Step 5: Subtract 36 from 40, bringing down pairs of zeros to continue the process.

Step 6: Repeat the process to find subsequent digits until the desired accuracy is reached.

The approximate value of √0.4 is 0.632455.

The approximation method is another way to find the square roots and is a straightforward method to find the square root of a given number. Let us learn how to find the square root of 2/5 using the approximation method.

Step 1: Convert 2/5 into a decimal, which is 0.4.

Step 2: Identify two perfect squares between which 0.4 lies. It lies between 0.36 (0.6^2) and 0.49 (0.7^2).

Step 3: Use interpolation to approximate the square root. Since 0.4 is closer to 0.36, we can start with an initial guess of 0.63.

Step 4: Refine the approximation by checking the squares of values around the initial guess until the desired precision is achieved.

Thus, the square root of 0.4 is approximately 0.632455.

• Square root: The square root is the number that, when multiplied by itself, gives the original number. Example: √(2/5) ≈ 0.632455.
   
• Rational number: A rational number can be expressed as a fraction of two integers, where the denominator is not zero.
   
• Irrational number: An irrational number cannot be expressed as a simple fraction; its decimal representation is non-repeating and non-terminating.
   
• Decimal: A number that consists of a whole number and a fractional part separated by a decimal point. For example, 0.632455 is a decimal.
   
• Fraction: A fraction represents a part of a whole or any number of equal parts, expressed as a/b, where 'a' is the numerator and 'b' is the denominator.