Simplify the Expression: (√35 × √20) ÷ √7

Q: Can I simplify each square root individually first?

While possible, it's much easier to use the product and quotient properties! Combining $ \sqrt{35} \cdot \sqrt{20} = \sqrt{700} $ keeps everything under radicals until the final step.

Q: What if I can't divide evenly inside the square root?

Great question! In this problem, $ \frac{700}{7} = 100 $ divides perfectly. If it didn't, you'd leave it as $ \sqrt{\text{result}} $ and see if you can simplify further.

Q: Why does the quotient property work here?

The quotient property states $ \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} $. This lets us move the division inside the square root, making calculations cleaner!

Q: How do I know when I have the final answer?

When you get a perfect square under the radical! Since $ \sqrt{100} = 10 $ exactly, we're done. No more radicals needed.

Q: What if I made an arithmetic error with 35 × 20?

Double-check: $ 35 \times 20 = 35 \times 2 \times 10 = 70 \times 10 = 700 $. Breaking it into steps helps avoid mistakes!

Radical Operations with Division Properties

$\frac{\sqrt{35}\cdot\sqrt{20}}{\sqrt{7}}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's solve this problem together.

00:12 First, break down 35, into factors of 7, and 5.

00:19 When you see a multiplication under a root, remember, you can factor it with the root.

00:32 Next, reduce wherever possible, to simplify.

00:41 Now, combine everything under one root for multiplication.

00:46 Calculate the multiplication carefully.

00:49 Factor 100, into 10, squared.

00:54 Notice how the root cancels the square.

00:58 And that's how we find the solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{\sqrt{35}\cdot\sqrt{20}}{\sqrt{7}}=$

Step-by-step solution

Let's begin the solution by applying the product property of square roots:

Combine the square roots in the numerator:

$\sqrt{35} \cdot \sqrt{20} = \sqrt{35 \cdot 20}$

Calculate $35 \cdot 20 = 700$ , so:

$\sqrt{35} \cdot \sqrt{20} = \sqrt{700}$

Now, divide this square root by the square root in the denominator using the quotient property:

$\frac{\sqrt{700}}{\sqrt{7}} = \sqrt{\frac{700}{7}}$

Simplify the fraction inside the square root:

$\frac{700}{7} = 100$

Thus, the expression becomes:

$\sqrt{100} = 10$

Therefore, the solution to the expression $\frac{\sqrt{35} \cdot \sqrt{20}}{\sqrt{7}}$ is $10$ .

The correct answer choice is:

$10$

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Product Rule: Combine square roots in numerator using multiplication property
Technique: Calculate $\sqrt{35} \cdot \sqrt{20} = \sqrt{700}$ first
Check: Verify $10^2 = 100 = \frac{700}{7}$ ✓

Common Mistakes

Avoid these frequent errors

Calculating each square root separately before combining
Don't find $\sqrt{35} = 5.92...$ and $\sqrt{20} = 4.47...$ first = messy decimals and rounding errors! This makes calculations harder and less accurate. Always use radical properties to combine under one square root before simplifying.

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

Can I simplify each square root individually first?

While possible, it's much easier to use the product and quotient properties! Combining $\sqrt{35} \cdot \sqrt{20} = \sqrt{700}$ keeps everything under radicals until the final step.

What if I can't divide evenly inside the square root?

Great question! In this problem, $\frac{700}{7} = 100$ divides perfectly. If it didn't, you'd leave it as $\sqrt{\text{result}}$ and see if you can simplify further.

Why does the quotient property work here?

The quotient property states $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ . This lets us move the division inside the square root, making calculations cleaner!

How do I know when I have the final answer?

When you get a perfect square under the radical! Since $\sqrt{100} = 10$ exactly, we're done. No more radicals needed.

What if I made an arithmetic error with 35 × 20?

Double-check: $35 \times 20 = 35 \times 2 \times 10 = 70 \times 10 = 700$ . Breaking it into steps helps avoid mistakes!

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Simplify the Expression: (√35 × √20) ÷ √7

Radical Operations with Division Properties

❤️ 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

Can I simplify each square root individually first?

What if I can't divide evenly inside the square root?

Why does the quotient property work here?

How do I know when I have the final answer?

What if I made an arithmetic error with 35 × 20?

🌟 Unlock Your Math Potential

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