Question

Find the approximate value of (25.2)^1/2.

Answer 1

We are tasked with finding the approximate value of \( (25.2)^{1/2} \), which is the square root of 25.2. To solve this, we can break it down into clear steps:

Step 1: Understand the expression: The notation \( (25.2)^{1/2} \) refers to the square root of 25.2. The square root of a number is a value that, when multiplied by itself, gives the original number. Therefore, we are looking for a value \( x \) such that: \[ x^2 = 25.2 \]

Step 2: Use a calculator or mathematical software: To find the square root of 25.2 accurately, we can use a calculator or mathematical software. Most scientific calculators or tools like Python, MATLAB, or even online calculators can help us compute square roots quickly and precisely. Using a calculator, we find: \[ \sqrt{25.2} \approx 5.02 \]

Step 3: Approximate the value: The square root of 25.2 is approximately 5.02. This is a rounded value, as the exact square root of 25.2 is a non-terminating decimal. Therefore, the approximate value of \( (25.2)^{1/2} \) is: \[ (25.2)^{1/2} \approx 5.02 \]

Step 4: Conclusion: The approximate value of \( (25.2)^{1/2} \) is 5.02. This approximation is sufficiently accurate for most practical purposes where exact values are not necessary.