Solve Square Root Problem: Simplifying √(64/4)

Q: Can I take the square root of the top and bottom separately?

While $ \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} $ is mathematically correct, it's easier and safer to simplify the fraction first. This prevents confusion and reduces calculation errors.

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

If $ \frac{64}{4} $ gave us something like 15 instead of 16, we'd leave the answer as $ \sqrt{15} $ or use a calculator to find the decimal approximation.

Q: Do I always have to simplify fractions first?

Yes! Simplifying fractions before taking square roots makes the problem much easier and helps you avoid calculation mistakes. Always divide first, then take the square root.

Q: What if I got 8 as my answer?

If you got 8, you likely found $ \sqrt{64} $ instead of $ \sqrt{\frac{64}{4}} $. Remember to divide 64 by 4 first to get 16, then find $ \sqrt{16} = 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

00:06 Let's solve this problem together.

00:09 First, we need to calculate the quotient.

00:14 We'll start by breaking down 16 into 4 to the power of 2.

00:19 Remember, the square root of any number, A to the power of 2, cancels out the square.

00:25 Let's apply this formula to our problem, and cancel out the square.

00:30 And there we have it! That's 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 the problem of finding $\sqrt{\frac{64}{4}}$ , we will proceed as follows:

Step 1: Simplify the fraction $\frac{64}{4}$ .
Step 2: Calculate the square root of the simplified result.

Let's work through these steps:

Step 1: Simplify the fraction.

The fraction given is $\frac{64}{4}$ . When we divide 64 by 4, we obtain 16.

So, $\frac{64}{4} = 16$ .

Step 2: Calculate the square root.

Now, we need to find $\sqrt{16}$ . We know that the square root of 16 is 4 because $4 \times 4 = 16$ .

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

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Simplify the fraction inside the radical before taking square root
Technique: $\frac{64}{4} = 16$ , then $\sqrt{16} = 4$
Check: Verify that $4 \times 4 = 16$ and $\frac{64}{4} = 16$ ✓

Common Mistakes

Avoid these frequent errors

Taking square root of numerator and denominator separately
Don't calculate $\frac{\sqrt{64}}{\sqrt{4}} = \frac{8}{2} = 4$ ! While this happens to give the correct answer here, it's not always true for all fractions. Always simplify the fraction first, then take the square root of the result.

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 take the square root of the top and bottom separately?

While $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ is mathematically correct, it's easier and safer to simplify the fraction first. This prevents confusion and reduces calculation errors.

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

If $\frac{64}{4}$ gave us something like 15 instead of 16, we'd leave the answer as $\sqrt{15}$ or use a calculator to find the decimal approximation.

How do I know 16 is a perfect square?

Perfect squares are numbers like 1, 4, 9, 16, 25, 36... Ask yourself: what number times itself equals 16? Since $4 \times 4 = 16$ , we know $\sqrt{16} = 4$ .

Do I always have to simplify fractions first?

Yes! Simplifying fractions before taking square roots makes the problem much easier and helps you avoid calculation mistakes. Always divide first, then take the square root.

What if I got 8 as my answer?

If you got 8, you likely found $\sqrt{64}$ instead of $\sqrt{\frac{64}{4}}$ . Remember to divide 64 by 4 first to get 16, then find $\sqrt{16} = 4$ .

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