Calculate the Square Root: Solving √225 Step by Step

Q: How do I know if 225 is a perfect square?

A number is a perfect square if it equals an integer multiplied by itself. Try numbers around where you think the answer might be: $ 14^2 = 196 $, $ 15^2 = 225 $ ✓

Q: What if I can't remember perfect squares?

Start with what you know! If you remember $ 10^2 = 100 $, try numbers between 10 and 20. Since 225 is much bigger than 100, try 15 or numbers near it.

Q: Is there a faster way than guessing and checking?

Estimation helps! Since $ 10^2 = 100 $ and $ 20^2 = 400 $, the answer must be between 10 and 20. Try the middle: 15!

Q: What's the difference between 15² and √225?

They're inverse operations! $ 15^2 $ means '15 times 15 equals 225', while $ \sqrt{225} $ means 'what number times itself equals 225?'

Q: Can square roots be negative?

The principal square root (what we usually want) is always positive. So $ \sqrt{225} = 15 $, not -15, even though $ (-15)^2 = 225 $ too.

Square Roots with Perfect Square Numbers

$\sqrt{225}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 The square root of any number (X) squared, root cancels square

00:18 We break down 225 to 15 squared

00:24 We will use this formula in our exercise

00:36 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\sqrt{225}=$

Step-by-step solution

To solve the problem, we will follow these steps:

Step 1: Identify the perfect squares near 225.
Step 2: Calculate to find which integer when squared equals 225.

Now, let's work through the steps:

Step 1: The perfect squares around 225 are $196 = 14^2$ , $225 = 15^2$ , and $256 = 16^2$ .
Step 2: We calculate $15^2 = 15 \times 15 = 225$ , therefore, $\sqrt{225} = 15$ .

Therefore, the solution to the problem is $\sqrt{225} = 15$ .

Accordingly, the correct answer choice is option 2: 15.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perfect Square Rule: Find integer that when squared gives the number
Technique: Test nearby squares: $15^2 = 15 \times 15 = 225$
Check: Verify answer by squaring: $15^2 = 225$ so $\sqrt{225} = 15$ ✓

Common Mistakes

Avoid these frequent errors

Dividing by 15 instead of finding what squares to 225
Don't divide 225 ÷ 15 = 15 thinking that's the square root! Division and square roots are different operations. Always ask 'what number times itself equals 225?' That's $15 \times 15 = 225$ .

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

How do I know if 225 is a perfect square?

A number is a perfect square if it equals an integer multiplied by itself. Try numbers around where you think the answer might be: $14^2 = 196$ , $15^2 = 225$ ✓

What if I can't remember perfect squares?

Start with what you know! If you remember $10^2 = 100$ , try numbers between 10 and 20. Since 225 is much bigger than 100, try 15 or numbers near it.

Is there a faster way than guessing and checking?

Estimation helps! Since $10^2 = 100$ and $20^2 = 400$ , the answer must be between 10 and 20. Try the middle: 15!

What's the difference between 15² and √225?

They're inverse operations! $15^2$ means '15 times 15 equals 225', while $\sqrt{225}$ means 'what number times itself equals 225?'

Can square roots be negative?

The principal square root (what we usually want) is always positive. So $\sqrt{225} = 15$ , not -15, even though $(-15)^2 = 225$ too.

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