Calculate the Square Root: Finding √100 Step by Step

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

A perfect square is created when you multiply an integer by itself. Common perfect squares to memorize: $ 1^2 = 1 $, $ 2^2 = 4 $, $ 3^2 = 9 $, $ 4^2 = 16 $, up to $ 10^2 = 100 $.

Q: What if I can't remember that 10² = 100?

Try counting up from smaller squares! Start with $ 5^2 = 25 $, then $ 8^2 = 64 $, then $ 9^2 = 81 $. Since 81 is close but not 100, try $ 10^2 $ next!

Q: Why isn't the answer 50 or 25?

Those would be if you divided 100, but square root is different! $ \sqrt{100} $ asks: what number times itself equals 100? Check: $ 50 \times 50 = 2500 $ (too big!), $ 25 \times 25 = 625 $ (still too big!).

Q: Are there any negative square roots?

While $ (-10)^2 = 100 $ is true, by convention $ \sqrt{100} $ refers to the positive square root only. So the answer is always 10, not -10.

Q: What's the fastest way to check my answer?

Simply multiply your answer by itself! If you think $ \sqrt{100} = 10 $, check: $ 10 \times 10 = 100 $ ✓. If it equals the original number, you're right!

Perfect Squares with Recognition Method

$\sqrt{100}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem together.

00:07 When you square root a number, then square it, the root cancels the square.

00:15 For example, we can see how one hundred is made by ten times ten.

00:20 Let's apply this idea to solve our exercise.

00:24 And that's how we find the answer to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\sqrt{100}=$

Step-by-step solution

The task is to find the square root of the number 100. The square root operation seeks a number which, when squared, equals the original number. For any positive integer, if $x^2 = 100$ , then $x$ should be our answer.

Step 1: Recognize that 100 is a perfect square. This means there exists an integer $x$ such that $x \times x = 100$ . Generally, we recall basic squares such as:

$1^2 = 1$
$2^2 = 4$
$3^2 = 9$
and so forth, up to $10^2$

Step 2: Checking integers, we find that:

$10^2 = 10 \times 10 = 100$

Step 3: Confirm the result: Since $10 \times 10 = 100$ , then $\sqrt{100} = 10$ .

Step 4: Compare with answer choices. Given that one of the choices is 10, and $\sqrt{100} = 10$ , choice 1 is correct.

Therefore, the square root of 100 is 10.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Square root asks what number times itself equals the given value
Technique: Recognize that $10^2 = 10 \times 10 = 100$
Check: Multiply your answer by itself: $10 \times 10 = 100$ ✓

Common Mistakes

Avoid these frequent errors

Confusing square root with division by 2
Don't divide 100 by 2 to get 50! This completely ignores what square root means. Square root means finding what number multiplied by itself gives 100. Always ask: what number times itself equals this value?

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

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

A perfect square is created when you multiply an integer by itself. Common perfect squares to memorize: $1^2 = 1$ , $2^2 = 4$ , $3^2 = 9$ , $4^2 = 16$ , up to $10^2 = 100$ .

What if I can't remember that 10² = 100?

Try counting up from smaller squares! Start with $5^2 = 25$ , then $8^2 = 64$ , then $9^2 = 81$ . Since 81 is close but not 100, try $10^2$ next!

Why isn't the answer 50 or 25?

Those would be if you divided 100, but square root is different! $\sqrt{100}$ asks: what number times itself equals 100? Check: $50 \times 50 = 2500$ (too big!), $25 \times 25 = 625$ (still too big!).

Are there any negative square roots?

While $(-10)^2 = 100$ is true, by convention $\sqrt{100}$ refers to the positive square root only. So the answer is always 10, not -10.

What's the fastest way to check my answer?

Simply multiply your answer by itself! If you think $\sqrt{100} = 10$ , check: $10 \times 10 = 100$ ✓. If it equals the original number, you're right!

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Calculate the Square Root: Finding √100 Step by Step

Perfect Squares with Recognition Method

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

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

What if I can't remember that 10² = 100?

Why isn't the answer 50 or 25?

Are there any negative square roots?

What's the fastest way to check my answer?

🌟 Unlock Your Math Potential

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