Calculate the Square Root: Finding √121 Step by Step

Q: How do I know if 121 is a perfect square?

A perfect square is a whole number that equals some integer multiplied by itself. Since $ 11 \times 11 = 121 $, we know 121 is a perfect square with root 11.

Q: What if I don't remember that 11 × 11 = 121?

Try testing numbers systematically! Start with $ 10^2 = 100 $ (too small), then $ 12^2 = 144 $ (too big), so the answer must be 11.

Q: Are there always two square roots for every number?

Yes! Every positive number has both a positive and negative square root. But when we write $ \sqrt{121} $, we mean the principal (positive) root, which is 11.

Q: Can I use a calculator to check my answer?

Absolutely! Use your calculator to verify that $ 11^2 = 121 $. This confirms that $ \sqrt{121} = 11 $.

Q: What's the difference between 121² and √121?

$ 121^2 $ means 121 × 121 = 14,641 (squaring), while $ \sqrt{121} $ means finding what number squared gives 121 (square root). They're opposite operations!

Perfect Square Roots with Integer Solutions

$\sqrt{121}=$

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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

00:13 We break down 121 to 11 squared

00:19 We will use this formula in our exercise

00:22 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

$\sqrt{121}=$

Step-by-step solution

To solve the problem of finding the square root of 121, let's follow these steps:

Step 1: Understand that we need to find a number $x$ such that $x^2 = 121$ .
Step 2: Recognize that 121 is a perfect square. Specifically, $11 \times 11 = 121$ .
Step 3: Therefore, the square root of 121 is clearly $11$ .

Thus, the solution to the problem is $11$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Find the number that multiplies by itself to equal 121
Recognition: Perfect squares like 121 = 11 × 11 have whole number roots
Verification: Check that 11 × 11 = 121 to confirm your answer ✓

Common Mistakes

Avoid these frequent errors

Confusing square root with division by 2
Don't divide 121 by 2 to get 60.5! Square root means finding what number times itself equals 121, not dividing by 2. Always ask: what number squared gives me 121?

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

How do I know if 121 is a perfect square?

A perfect square is a whole number that equals some integer multiplied by itself. Since $11 \times 11 = 121$ , we know 121 is a perfect square with root 11.

What if I don't remember that 11 × 11 = 121?

Try testing numbers systematically! Start with $10^2 = 100$ (too small), then $12^2 = 144$ (too big), so the answer must be 11.

Are there always two square roots for every number?

Yes! Every positive number has both a positive and negative square root. But when we write $\sqrt{121}$ , we mean the principal (positive) root, which is 11.

Can I use a calculator to check my answer?

Absolutely! Use your calculator to verify that $11^2 = 121$ . This confirms that $\sqrt{121} = 11$ .

What's the difference between 121² and √121?

$121^2$ means 121 × 121 = 14,641 (squaring), while $\sqrt{121}$ means finding what number squared gives 121 (square root). They're opposite operations!

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