Solve Square Root of 1/36: Simplifying Radical Fractions

Q: Why can I split the square root across the fraction?

This works because of the square root property for fractions: $ \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} $. Just like how multiplication splits across fractions, square roots do too!

Q: What if the numerator or denominator isn't a perfect square?

You can still apply the same property! For example: $ \sqrt{\frac{2}{9}} = \frac{\sqrt{2}}{\sqrt{9}} = \frac{\sqrt{2}}{3} $. Leave any non-perfect squares in radical form.

Q: Can I simplify this a different way?

Yes! You could also think: $ \sqrt{\frac{1}{36}} = \sqrt{\frac{1^2}{6^2}} = \frac{1}{6} $. Both methods give the same answer.

Q: What if I got a decimal instead of a fraction?

While $ \frac{1}{6} \approx 0.167 $ is correct, keep your answer as a fraction unless specifically asked for a decimal. Fractions are usually the preferred exact form.

Square Roots with Fractional Expressions

Complete the following exercise:

$\sqrt{\frac{1}{36}}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's work on solving this problem together.

00:10 We have the root of a fraction, A divided by B.

00:14 This is the same as the root of the numerator, A, divided by the root of the denominator, B.

00:20 Now, let's apply this formula to our example.

00:24 Break down thirty-six into six squared.

00:30 Remember, the root of any number, A, squared cancels out the square.

00:35 Use this formula in our exercise to cancel out the squares.

00:40 And there you have it, the solution is complete!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following exercise:

$\sqrt{\frac{1}{36}}=$

Step-by-step solution

In order to determine the square root of the following fraction $\frac{1}{36}$ , we will apply the square root property for fractions. This property states that the square root of a fraction is the fraction of the square roots of the numerator and the denominator. Let's follow these steps:

Step 1: Identify the given fraction, which is $\frac{1}{36}$ .
Step 2: Apply the square root property as follows $\sqrt{\frac{1}{36}} = \frac{\sqrt{1}}{\sqrt{36}}$ .
Step 3: Calculate the square root of the numerator: $\sqrt{1} = 1$ .
Step 4: Calculate the square root of the denominator: $\sqrt{36} = 6$ .
Step 5: Form the fraction: $\frac{1}{6}$ .

By following these steps, we have successfully simplified the expression. Therefore, the square root of $\frac{1}{36}$ is $\frac{1}{6}$ .

Thus, the correct and final answer to the problem $\sqrt{\frac{1}{36}} =$ is $\frac{1}{6}$ .

Final Answer

$\frac{1}{6}$

Key Points to Remember

Essential concepts to master this topic

Property: Square root of fraction equals fraction of square roots
Technique: $\sqrt{\frac{1}{36}} = \frac{\sqrt{1}}{\sqrt{36}} = \frac{1}{6}$
Check: Verify by squaring: $\left(\frac{1}{6}\right)^2 = \frac{1}{36}$ ✓

Common Mistakes

Avoid these frequent errors

Taking square root of numerator and denominator separately then adding
Don't calculate $\sqrt{1} + \sqrt{36} = 1 + 6 = 7$ ! This gives completely wrong results because you're adding instead of forming a fraction. Always apply the property: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ .

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

Why can I split the square root across the fraction?

This works because of the square root property for fractions: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ . Just like how multiplication splits across fractions, square roots do too!

What if the numerator or denominator isn't a perfect square?

You can still apply the same property! For example: $\sqrt{\frac{2}{9}} = \frac{\sqrt{2}}{\sqrt{9}} = \frac{\sqrt{2}}{3}$ . Leave any non-perfect squares in radical form.

How do I know if 36 is a perfect square?

Think about multiplication facts: 6 × 6 = 36, so $\sqrt{36} = 6$ . Perfect squares are numbers like 1, 4, 9, 16, 25, 36, 49...

Can I simplify this a different way?

Yes! You could also think: $\sqrt{\frac{1}{36}} = \sqrt{\frac{1^2}{6^2}} = \frac{1}{6}$ . Both methods give the same answer.

What if I got a decimal instead of a fraction?

While $\frac{1}{6} \approx 0.167$ is correct, keep your answer as a fraction unless specifically asked for a decimal. Fractions are usually the preferred exact form.

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