Calculate the Square Root of 100/4: Step-by-Step Solution

Q: Can I just divide 100 by 4 first, then take the square root?

Yes, that works for this problem! $ \frac{100}{4} = 25 $, so $ \sqrt{25} = 5 $. But learning the quotient property helps with harder problems where the numbers don't divide evenly.

Q: What if the numbers under the square root don't have perfect square roots?

The quotient property still works! For example, $ \sqrt{\frac{50}{8}} = \frac{\sqrt{50}}{\sqrt{8}} $. You can then simplify each square root separately using factors.

Q: Why do we use the quotient property instead of just calculating?

The quotient property is a fundamental rule that works for all square root fractions. It helps you understand the structure and makes complex problems easier to solve step-by-step.

Q: How do I remember which square roots to calculate first?

Always work with the numerator and denominator separately! Find $ \sqrt{100} $ and $ \sqrt{4} $ independently, then divide the results.

Q: What if I get a different answer using a different method?

If you get different answers, check your work! Both the quotient property and "divide first" methods should give the same result. Square your final answer to verify: $ 5^2 = 25 $ and $ \frac{100}{4} = 25 $ ✓

Square Root Properties with Quotient Rule

Solve the following exercise:

$\sqrt{\frac{100}{4}}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve this problem together.

00:11 We need the square root of the fraction A divided by B.

00:15 This is the same as the square root of A, divided by the square root of B.

00:20 Let's apply this idea to our example.

00:26 First, break down 100 into 10 squared.

00:31 Then, break down 4 into 2 squared.

00:35 Remember, the square root of any squared number just cancels out the square.

00:40 Let's use this to simplify our problem and cancel out the squares.

00:45 And there you have it, that's our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\sqrt{\frac{100}{4}}=$

Step-by-step solution

To solve this problem, we'll apply the Square Root Quotient Property to the given expression. The property states that:

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

Let's apply this property to the expression $\sqrt{\frac{100}{4}}$ :

Step 1: Calculate $\sqrt{100}$ . The square root of 100 is 10, because $10 \times 10 = 100$ .
Step 2: Calculate $\sqrt{4}$ . The square root of 4 is 2, because $2 \times 2 = 4$ .
Step 3: Divide the results from Step 1 and Step 2, using the formula:
$\frac{\sqrt{100}}{\sqrt{4}} = \frac{10}{2} = 5$

Therefore, the solution to the problem is $\boxed{5}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Quotient Rule: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ separates the fraction
Technique: Calculate $\sqrt{100} = 10$ and $\sqrt{4} = 2$ separately
Check: Verify that $5^2 = 25$ equals $\frac{100}{4} = 25$ ✓

Common Mistakes

Avoid these frequent errors

Calculating the fraction first then taking square root
Don't calculate 100 ÷ 4 = 25, then √25 = 5! While this gives the right answer here, it's harder with complex fractions and you miss learning the quotient property. Always use the quotient rule to separate √a and √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 divide 100 by 4 first, then take the square root?

Yes, that works for this problem! $\frac{100}{4} = 25$ , so $\sqrt{25} = 5$ . But learning the quotient property helps with harder problems where the numbers don't divide evenly.

What if the numbers under the square root don't have perfect square roots?

The quotient property still works! For example, $\sqrt{\frac{50}{8}} = \frac{\sqrt{50}}{\sqrt{8}}$ . You can then simplify each square root separately using factors.

Why do we use the quotient property instead of just calculating?

The quotient property is a fundamental rule that works for all square root fractions. It helps you understand the structure and makes complex problems easier to solve step-by-step.

How do I remember which square roots to calculate first?

Always work with the numerator and denominator separately! Find $\sqrt{100}$ and $\sqrt{4}$ independently, then divide the results.

What if I get a different answer using a different method?

If you get different answers, check your work! Both the quotient property and "divide first" methods should give the same result. Square your final answer to verify: $5^2 = 25$ and $\frac{100}{4} = 25$ ✓

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