Solve Square Root of Fraction: √(64/4) Simplified

Q: Should I simplify the fraction first or use the quotient property?

Both methods work, but simplifying first is usually easier! $ \frac{64}{4} = 16 $, so $ \sqrt{16} = 4 $ is simpler than calculating $ \frac{\sqrt{64}}{\sqrt{4}} $.

Q: What if the fraction doesn't simplify to a perfect square?

Then use the quotient property: $ \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} $. Find the square roots of numerator and denominator separately, then divide the results.

Q: Can I have a decimal answer for square roots of fractions?

Yes! Not all square roots are whole numbers. If you get a decimal, that's often the correct answer. Just make sure to check your work by squaring the decimal result.

Q: What's the difference between √(64/4) and √64/√4?

They're the same thing! The quotient property says $ \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} $, so both expressions equal 4.

Square Root Operations with Fraction Simplification

Solve the following exercise:

$\sqrt{\frac{64}{4}}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 The root of a fraction (A divided by B)

00:06 Equals the root of the numerator (A) divided by the root of the denominator (B)

00:11 Apply this formula to our exercise

00:15 Break down 64 to 8 squared

00:20 Break down 4 to 2 squared

00:24 The root of any number (A) squared cancels out the square

00:27 Apply this formula to our exercise and proceed to cancel out the square

00:35 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\sqrt{\frac{64}{4}}=$

Step-by-step solution

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

Step 1: Simplify the fraction $\frac{64}{4}$ .
Step 2: Apply the Square Root Quotient Property.
Step 3: Calculate the square roots of the numerator and the denominator.

Now, let's work through each step:

Step 1: Simplify the fraction $\frac{64}{4}$ . The division yields $16$ , so we have $\sqrt{16}$ .

Step 2: Using the Square Root Quotient Property, $\sqrt{\frac{64}{4}} = \frac{\sqrt{64}}{\sqrt{4}}$ .

Step 3: Calculate the square roots: $\sqrt{64} = 8$ and $\sqrt{4} = 2$ , so $\frac{8}{2} = 4$ .

Thus, the solution to the problem is $\sqrt{\frac{64}{4}} = 4$ .

Therefore, the correct answer is $4$ , which corresponds to choice 3 in the given options.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Simplify the fraction inside the radical first before calculating
Technique: Use quotient property: $\sqrt{\frac{64}{4}} = \frac{\sqrt{64}}{\sqrt{4}} = \frac{8}{2} = 4$
Check: Verify by squaring your answer: $4^2 = 16 = \frac{64}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Calculating square roots before simplifying the fraction
Don't jump straight to $\frac{\sqrt{64}}{\sqrt{4}}$ without first checking if the fraction simplifies = unnecessary complexity! You miss the easier path of $\sqrt{16} = 4$ . Always simplify fractions first, then apply square root operations.

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

Should I simplify the fraction first or use the quotient property?

Both methods work, but simplifying first is usually easier! $\frac{64}{4} = 16$ , so $\sqrt{16} = 4$ is simpler than calculating $\frac{\sqrt{64}}{\sqrt{4}}$ .

What if the fraction doesn't simplify to a perfect square?

Then use the quotient property: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ . Find the square roots of numerator and denominator separately, then divide the results.

How do I know if my square root answer is correct?

Square your answer and check if it equals the original expression under the radical. For example: $4^2 = 16$ , and $\frac{64}{4} = 16$ ✓

Can I have a decimal answer for square roots of fractions?

Yes! Not all square roots are whole numbers. If you get a decimal, that's often the correct answer. Just make sure to check your work by squaring the decimal result.

What's the difference between √(64/4) and √64/√4?

They're the same thing! The quotient property says $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ , so both expressions equal 4.

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