Evaluate the Square Root Expression: √49

Q: Why isn't the answer -7 since (-7) × (-7) = 49?

Great observation! While both 7 and -7 when squared equal 49, the square root symbol $ \sqrt{} $ by convention means the positive square root only.

Q: Is there a trick for checking my answer quickly?

Yes! Simply square your answer and see if you get the original number. If $ \sqrt{49} = 7 $, then 7² should equal 49.

Q: What happens if the number under the square root isn't a perfect square?

Then the answer won't be a whole number! For example, $ \sqrt{50} $ is between 7 and 8. But for now, focus on perfect squares like this problem.

Square Root Evaluation with Perfect Squares

$\sqrt{49}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

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

00:10 We break down 49 to 7 squared

00:16 We'll use this formula in our exercise

00:19 Root and square cancel each other

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

$\sqrt{49}=$

Step-by-step solution

To solve this problem, we follow these steps:

Step 1: Understand that finding the square root of a number means determining what number, when multiplied by itself, equals the original number.
Step 2: Identify the numbers that could potentially be the square root of $49$ . These are $\pm7$ , but by convention, the square root function typically refers to the non-negative root.
Step 3: Calculate $7 \times 7 = 49$ . This confirms that $\sqrt{49} = 7$ .
Step 4: Verify using the problem's multiple-choice answers to ensure $7$ is among them, confirming choice number .

Therefore, the solution to the problem $\sqrt{49}$ is $7$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Square root asks what number times itself equals the given number
Technique: Test 7 × 7 = 49 to verify $\sqrt{49} = 7$
Check: Multiply your answer by itself: 7 × 7 = 49 ✓

Common Mistakes

Avoid these frequent errors

Confusing square root with division by 2
Don't divide 49 ÷ 2 = 24.5! This is completely wrong because square root means finding what number multiplied by itself gives 49, not half of 49. Always ask yourself: what times what equals 49?

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

Why isn't the answer -7 since (-7) × (-7) = 49?

Great observation! While both 7 and -7 when squared equal 49, the square root symbol $\sqrt{}$ by convention means the positive square root only.

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

A perfect square is a whole number that equals another whole number times itself. Common ones to memorize: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Practice these!

What if I can't remember if 49 is a perfect square?

Try counting up: 1×1=1, 2×2=4, 3×3=9... keep going until you reach 7×7=49. This helps you discover the answer rather than just memorizing!

Is there a trick for checking my answer quickly?

Yes! Simply square your answer and see if you get the original number. If $\sqrt{49} = 7$ , then 7² should equal 49.

What happens if the number under the square root isn't a perfect square?

Then the answer won't be a whole number! For example, $\sqrt{50}$ is between 7 and 8. But for now, focus on perfect squares like this problem.

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