Calculate the Square Root: Finding √0.25

Q: Why should I convert 0.25 to a fraction instead of working with the decimal?

Converting to a fraction makes the square root much clearer! When you see $ \frac{1}{4} $, it's obvious that $ \sqrt{\frac{1}{4}} = \frac{1}{2} $. Working directly with 0.25 requires memorization or guessing.

Q: How do I convert 0.25 to a fraction?

Easy method: 0.25 means 25 out of 100, so $ 0.25 = \frac{25}{100} $. Then simplify by dividing both numbers by 25 to get $ \frac{1}{4} $!

Q: What if I don't know the square root of the numerator or denominator?

For basic problems like this, you should recognize that $ \sqrt{1} = 1 $ and $ \sqrt{4} = 2 $. Practice memorizing perfect square numbers like 1, 4, 9, 16, 25, 36, etc.

Q: How can I check if 0.5 is really the right answer?

Simple! Just square your answer: $ (0.5)^2 = 0.5 \times 0.5 = 0.25 $. Since this equals the original number under the square root, you know 0.5 is correct!

Q: Are there other ways to think about this problem?

Yes! You can also think: "What number times itself gives 0.25?" Since $ 0.5 \times 0.5 = 0.25 $, the answer is 0.5. This is exactly what square root means!

Square Roots with Decimal Numbers

$\sqrt{0.25}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve the problem step by step.

00:10 First, consider zero point two five as zero point five squared.

00:15 Remember, taking the square root of X squared cancels the square.

00:19 And that's how we find the solution to this question. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\sqrt{0.25}=$

Step-by-step solution

To solve this problem, we need to find the square root of $0.25$ . We will follow these steps:

Step 1: Convert $0.25$ to a more manageable form: $0.25 = \frac{25}{100} = \frac{1}{4}$ .
Step 2: Use the property of square roots: If $\sqrt{\frac{1}{4}} = y$ , then $y^2 = \frac{1}{4}$ .

Now, let's calculate the square root:
Since $\frac{1}{4}$ is a fraction, taking the square root of a fraction involves taking the square root of the numerator and the square root of the denominator separately:
$\sqrt{\frac{1}{4}} = \frac{\sqrt{1}}{\sqrt{4}} = \frac{1}{2}$ .

Verify by squaring the result: $(\frac{1}{2})^2 = \frac{1}{4}$ . This matches the original number, confirming our result is correct.

Therefore, the square root of $0.25$ is $0.5$ .

Final Answer

0.5

Key Points to Remember

Essential concepts to master this topic

Rule: Convert decimals to fractions for easier square root calculation
Technique: $0.25 = \frac{1}{4}$ , so $\sqrt{0.25} = \frac{1}{2} = 0.5$
Check: Square your answer: $(0.5)^2 = 0.25$ matches the original ✓

Common Mistakes

Avoid these frequent errors

Guessing without understanding the decimal-fraction connection
Don't just guess random decimals like 0.625 or 0.05! This leads to wrong answers because you're not using the mathematical relationship. Always convert 0.25 to its fraction form 1/4 first, then find the square root systematically.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

Why should I convert 0.25 to a fraction instead of working with the decimal?

Converting to a fraction makes the square root much clearer! When you see $\frac{1}{4}$ , it's obvious that $\sqrt{\frac{1}{4}} = \frac{1}{2}$ . Working directly with 0.25 requires memorization or guessing.

How do I convert 0.25 to a fraction?

Easy method: 0.25 means 25 out of 100, so $0.25 = \frac{25}{100}$ . Then simplify by dividing both numbers by 25 to get $\frac{1}{4}$ !

What if I don't know the square root of the numerator or denominator?

For basic problems like this, you should recognize that $\sqrt{1} = 1$ and $\sqrt{4} = 2$ . Practice memorizing perfect square numbers like 1, 4, 9, 16, 25, 36, etc.

How can I check if 0.5 is really the right answer?

Simple! Just square your answer: $(0.5)^2 = 0.5 \times 0.5 = 0.25$ . Since this equals the original number under the square root, you know 0.5 is correct!

Are there other ways to think about this problem?

Yes! You can also think: "What number times itself gives 0.25?" Since $0.5 \times 0.5 = 0.25$ , the answer is 0.5. This is exactly what square root means!

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