Solve Square Root Division: √64/√16 Simplification Exercise

Q: Can I just calculate √64 and √16 separately first?

Yes, both methods work for perfect squares like 64 and 16! However, using the quotient property $ \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} $ is more efficient and essential for harder problems with non-perfect squares.

Q: What if the numbers under the square roots don't divide evenly?

The quotient property still works! For example, $ \frac{\sqrt{50}}{\sqrt{8}} = \sqrt{\frac{50}{8}} = \sqrt{6.25} = 2.5 $. You can always simplify the fraction first.

Q: Why does the quotient property work?

Think of it this way: $ \frac{\sqrt{a}}{\sqrt{b}} $ asks "what number times $ \sqrt{b} $ gives $ \sqrt{a} $?" The answer is $ \sqrt{\frac{a}{b}} $ because square root properties preserve division.

Q: Do I always need to use this property for square root division?

Not always, but it's very helpful! With perfect squares like in this problem, either method works. But for complex expressions or non-perfect squares, the quotient property makes calculations much easier.

Q: What if there's a zero in the denominator?

Just like regular division, never divide by zero! If $ \sqrt{b} = 0 $, then b = 0, and the expression $ \frac{\sqrt{a}}{\sqrt{0}} $ is undefined.

Square Root Division with Quotient Property

Solve the following exercise:

$\frac{\sqrt{64}}{\sqrt{16}}=$

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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 Break down 64 to 8 squared

00:06 Break down 16 to 4 squared

00:11 The square root of any number (A) squared cancels out the square

00:15 Apply this formula to our exercise and proceed to cancel out the squares

00:23 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:

$\frac{\sqrt{64}}{\sqrt{16}}=$

Step-by-step solution

To solve the expression $\frac{\sqrt{64}}{\sqrt{16}}$ , we will use the square root quotient property, which states:

$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ , assuming $b \neq 0$ .

Applying this property, we have:

$\frac{\sqrt{64}}{\sqrt{16}} = \sqrt{\frac{64}{16}}$ .

Next, we calculate the division within the square root:

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

Therefore, we now find the square root of 4:

$\sqrt{4} = 2$ .

Hence, the result of the original expression $\frac{\sqrt{64}}{\sqrt{16}}$ is $\mathbf{2}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: Division of square roots equals square root of quotient
Technique: $\frac{\sqrt{64}}{\sqrt{16}} = \sqrt{\frac{64}{16}} = \sqrt{4}$
Check: Verify $\sqrt{64} = 8$ and $\sqrt{16} = 4$ , so $\frac{8}{4} = 2$ ✓

Common Mistakes

Avoid these frequent errors

Computing square roots first then dividing
Don't calculate $\sqrt{64} = 8$ and $\sqrt{16} = 4$ separately before dividing! While this gives the correct answer (8÷4=2), it's inefficient and can lead to errors with non-perfect squares. Always use the quotient property: $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ first.

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 just calculate √64 and √16 separately first?

Yes, both methods work for perfect squares like 64 and 16! However, using the quotient property $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ is more efficient and essential for harder problems with non-perfect squares.

What if the numbers under the square roots don't divide evenly?

The quotient property still works! For example, $\frac{\sqrt{50}}{\sqrt{8}} = \sqrt{\frac{50}{8}} = \sqrt{6.25} = 2.5$ . You can always simplify the fraction first.

Why does the quotient property work?

Think of it this way: $\frac{\sqrt{a}}{\sqrt{b}}$ asks "what number times $\sqrt{b}$ gives $\sqrt{a}$ ?" The answer is $\sqrt{\frac{a}{b}}$ because square root properties preserve division.

Do I always need to use this property for square root division?

Not always, but it's very helpful! With perfect squares like in this problem, either method works. But for complex expressions or non-perfect squares, the quotient property makes calculations much easier.

What if there's a zero in the denominator?

Just like regular division, never divide by zero! If $\sqrt{b} = 0$ , then b = 0, and the expression $\frac{\sqrt{a}}{\sqrt{0}}$ is undefined.

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