Solve the Square Root Expression: √25 Step-by-Step

Q: Why isn't the answer -5 since (-5) × (-5) = 25 too?

Great observation! While $ (-5) \times (-5) = 25 $ is true, the square root symbol √ always means the positive square root by convention. So $ \sqrt{25} = 5 $, not -5.

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

Perfect squares are numbers like 1, 4, 9, 16, 25, 36... Try multiplying small whole numbers by themselves: $ 1^2 = 1 $, $ 2^2 = 4 $, $ 3^2 = 9 $, etc.

Q: What if I can't figure out what number times itself equals the given number?

Start with small numbers and work up! For √25, try: $ 1 \times 1 = 1 $ (too small), $ 2 \times 2 = 4 $ (too small), keep going until you reach $ 5 \times 5 = 25 $ (perfect!).

Q: Can I use a calculator for square roots?

Yes, but try to recognize common perfect squares first! Knowing that $ \sqrt{1} = 1 $, $ \sqrt{4} = 2 $, $ \sqrt{9} = 3 $, $ \sqrt{16} = 4 $, $ \sqrt{25} = 5 $ will save you time!

Q: Is there a difference between √25 and 25^(1/2)?

No difference at all! $ \sqrt{25} $ and $ 25^{1/2} $ are just two different ways to write the same thing. Both equal 5.

Square Root Operations with Perfect Squares

$\sqrt{25}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 The square root of any number (X) squared, root cancels square

00:10 We break down 25 to 5 squared

00:17 We will use this formula in our exercise

00:21 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

$\sqrt{25}=$

Step-by-step solution

To solve this problem, we need to determine the square root of 25.

Step 1: The square root operation asks us to find a number that, when multiplied by itself, equals the given number, 25.
Step 2: Consider what number times itself equals 25. We note that $5 \times 5 = 25$ .
Step 3: Thus, the square root of 25 is 5.

Therefore, the solution to the problem is $\sqrt{25} = 5$ .

The correct answer is choice 2: 5.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Square root finds number that multiplies by itself
Technique: Ask what number times itself equals 25: $5 \times 5 = 25$
Check: Verify by squaring your answer: $5^2 = 25$ ✓

Common Mistakes

Avoid these frequent errors

Confusing square root with division by 2
Don't divide 25 by 2 to get 12.5 = wrong answer! Square root is NOT division. Always ask 'what number times itself equals 25?' to find the correct square root.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

Why isn't the answer -5 since (-5) × (-5) = 25 too?

Great observation! While $(-5) \times (-5) = 25$ is true, the square root symbol √ always means the positive square root by convention. So $\sqrt{25} = 5$ , not -5.

How do I know if a number is a perfect square?

Perfect squares are numbers like 1, 4, 9, 16, 25, 36... Try multiplying small whole numbers by themselves: $1^2 = 1$ , $2^2 = 4$ , $3^2 = 9$ , etc.

What if I can't figure out what number times itself equals the given number?

Start with small numbers and work up! For √25, try: $1 \times 1 = 1$ (too small), $2 \times 2 = 4$ (too small), keep going until you reach $5 \times 5 = 25$ (perfect!).

Can I use a calculator for square roots?

Yes, but try to recognize common perfect squares first! Knowing that $\sqrt{1} = 1$ , $\sqrt{4} = 2$ , $\sqrt{9} = 3$ , $\sqrt{16} = 4$ , $\sqrt{25} = 5$ will save you time!

Is there a difference between √25 and 25^(1/2)?

No difference at all! $\sqrt{25}$ and $25^{1/2}$ are just two different ways to write the same thing. Both equal 5.

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