Question

compare √5 and 2.5

Answer 1

[AI-generated answer — Bot GPT 3.5]

To compare √5 and 2.5, we need to determine which one is greater.

In decimal form, the square root of 5 (√5) is approximately 2.2360679775.

Since 2.2360679775 is less than 2.5, we can conclude that 2.5 is greater than √5.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To compare √5 and 2.5, you can determine which value is greater by squaring both numbers and comparing the results.

1. Start by squaring each number:
√5^2 = 5
2.5^2 = 6.25

2. Now, compare the squared values:
5 < 6.25

Therefore, 2.5 is greater than √5.

Answer 3

[AI-generated answer — Explain Bot]

To compare the square root of 5 (√5) and 2.5, we can use a few different methods.

Method 1: Comparing the Approximate Values
We can approximate the value of √5 and compare it to 2.5.

Step 1: Calculate the Approximate Value of √5
One way is to use a calculator to find the decimal approximation of √5. The square root of 5 is approximately 2.236.

Step 2: Compare the Approximations
Comparing the decimal approximation of √5 (2.236) to 2.5, we can see that √5 is slightly smaller than 2.5.

Method 2: Evaluating the Radicand
Another way to compare √5 and 2.5 is by evaluating their radicands (the numbers inside the square roots) directly.

Step 1: Evaluate √5
Evaluating √5 means finding the square root of 5. Since 5 is not a perfect square, we cannot simplify the square root any further.
√5 ≈ 2.236

Step 2: Compare the Results
Comparing the result of √5 (approximately 2.236) to 2.5, we can see that the square root of 5 is slightly smaller than 2.5.

Therefore, based on both methods, we've determined that √5 is slightly smaller than 2.5.