Evaluate the Expression: Square Root of 49 Divided by 7

Q: How do I know if 49 is a perfect square?

A perfect square is a number that equals some integer times itself. Since $ 7 \times 7 = 49 $, we know 49 is a perfect square and $ \sqrt{49} = 7 $.

Q: What's the difference between √(49/7) and √49/7?

These are completely different! $ \sqrt{\frac{49}{7}} = \sqrt{7} \approx 2.65 $, but $ \frac{\sqrt{49}}{7} = \frac{7}{7} = 1 $. Order of operations matters!

Square Root Evaluation with Perfect Squares

Solve the following exercise:

$\frac{\sqrt{49}}{7}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this math problem together.

00:10 First, we express 49 as 7 to the power of 2.

00:14 Remember, the square root of a number A squared, removes the square.

00:19 Now, apply this idea here. Cancel out the square, and move forward.

00:25 Great job! This is the solution. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{\sqrt{49}}{7}=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Calculate the square root of 49.
Step 2: Divide the result by 7.

Now, let's work through each step:
Step 1: Calculate the square root of 49. We have $\sqrt{49}$ . Since 49 is a perfect square, the square root of 49 is $7$ , because $7 \times 7 = 49$ .
Step 2: Divide the result obtained in Step 1 by 7. So we have: $\frac{\sqrt{49}}{7} = \frac{7}{7}$

The result of this division is $1$ , because dividing any number by itself (except zero) yields 1.

Therefore, the solution to the problem is $1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Perfect Squares: Recognize 49 = 7² to find √49 = 7
Order of Operations: Calculate √49 first, then divide: 7 ÷ 7
Check: Verify √49 = 7 by confirming 7 × 7 = 49 ✓

Common Mistakes

Avoid these frequent errors

Dividing under the radical sign first
Don't try to calculate √(49/7) = √7 ≈ 2.65! This changes the problem completely and gives the wrong answer. Always follow order of operations: calculate the square root first, then divide the result by 7.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\sqrt{\frac{2}{4}}=$

FAQ

Everything you need to know about this question

How do I know if 49 is a perfect square?

A perfect square is a number that equals some integer times itself. Since $7 \times 7 = 49$ , we know 49 is a perfect square and $\sqrt{49} = 7$ .

Can I use a calculator for square roots?

Yes, but for perfect squares like 49, 36, 64, it's faster to memorize them! Practice recognizing perfect squares from 1² to 12² - it will speed up your math significantly.

What's the difference between √(49/7) and √49/7?

These are completely different! $\sqrt{\frac{49}{7}} = \sqrt{7} \approx 2.65$ , but $\frac{\sqrt{49}}{7} = \frac{7}{7} = 1$ . Order of operations matters!

Why does 7 ÷ 7 equal 1?

Any number divided by itself equals 1 (except zero). This is because $\frac{7}{7}$ means "how many groups of 7 fit into 7?" The answer is exactly 1 group.

What if I forgot that √49 = 7?

Think of multiplication tables! What number times itself gives 49? Start checking: 6×6=36, 7×7=49, 8×8=64. So $\sqrt{49} = 7$ .

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