Solve Square Root Division: √144 ÷ √4 Simplification Problem

Q: Can I solve this by finding each square root first?

Yes, you can! $ \sqrt{144} = 12 $ and $ \sqrt{4} = 2 $, so $ \frac{12}{2} = 6 $. However, using the quotient property is more elegant and helps with harder problems.

Q: What is the square root quotient property?

The quotient property states that $ \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} $. This lets you combine division under one radical, making calculations simpler!

Q: How do I know if 144 and 4 are perfect squares?

Look for numbers you can multiply by themselves: $ 12 \times 12 = 144 $ and $ 2 \times 2 = 4 $. Practice memorizing perfect squares from 1 to 144 to solve these faster!

Q: Why is √6 not the correct answer?

$ \sqrt{6} $ would be correct if we had $ \sqrt{\frac{144}{4}} = \sqrt{36} $. But $ \sqrt{36} = 6 $, not $ \sqrt{6} $! Always simplify completely.

Q: Can this method work with non-perfect squares?

Absolutely! For example, $ \frac{\sqrt{8}}{\sqrt{2}} = \sqrt{\frac{8}{2}} = \sqrt{4} = 2 $. The quotient property works with any positive numbers under the radicals.

Square Root Division with Quotient Property

Solve the following exercise:

$\frac{\sqrt{144}}{\sqrt{4}}=$

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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 step by step!

00:11 First, notice that one hundred forty-four can be written as twelve squared.

00:17 Next, remember that four can be written as two squared.

00:21 The square root of a number squared will cancel the square, leaving just the number.

00:26 Let's use this formula in our problem and remove the squares.

00:32 Great job! We've found our solution. Keep practicing, and you'll get even better.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{\sqrt{144}}{\sqrt{4}}=$

Step-by-step solution

We are tasked with solving the expression $\frac{\sqrt{144}}{\sqrt{4}}$ . To proceed, we will use the square root quotient property.

According to the square root quotient property, $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ . Applying this to the given expression, we have:

\frac{\sqrt{144}}{\sqrt{4}} = \sqrt{\frac{144}{4}}

Next, simplify the fraction inside the square root:

\frac{144}{4} = 36

Now, we need to find the square root of 36:

\sqrt{36} = 6

Thus, the value of $\frac{\sqrt{144}}{\sqrt{4}}$ is $6$ .

Therefore, the solution to the problem is $\boxed{6}$ .

Final Answer

$6$

Key Points to Remember

Essential concepts to master this topic

Quotient Property: $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ combines division under one radical
Technique: Simplify $\frac{144}{4} = 36$ first, then find $\sqrt{36} = 6$
Check: Verify $\frac{12}{2} = 6$ by calculating each square root separately ✓

Common Mistakes

Avoid these frequent errors

Calculating each square root separately without using the quotient property
Don't compute $\sqrt{144} = 12$ and $\sqrt{4} = 2$ then divide = more work and potential errors! While this gives the correct answer, it's inefficient and misses the elegant quotient property. Always use $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ to combine under one radical first.

Practice Quiz

Test your knowledge with interactive questions

Choose the expression that is equal to the following:

$\sqrt{a}:\sqrt{b}$

FAQ

Everything you need to know about this question

Can I solve this by finding each square root first?

Yes, you can! $\sqrt{144} = 12$ and $\sqrt{4} = 2$ , so $\frac{12}{2} = 6$ . However, using the quotient property is more elegant and helps with harder problems.

What is the square root quotient property?

The quotient property states that $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ . This lets you combine division under one radical, making calculations simpler!

How do I know if 144 and 4 are perfect squares?

Look for numbers you can multiply by themselves: $12 \times 12 = 144$ and $2 \times 2 = 4$ . Practice memorizing perfect squares from 1 to 144 to solve these faster!

Why is √6 not the correct answer?

$\sqrt{6}$ would be correct if we had $\sqrt{\frac{144}{4}} = \sqrt{36}$ . But $\sqrt{36} = 6$ , not $\sqrt{6}$ ! Always simplify completely.

Can this method work with non-perfect squares?

Absolutely! For example, $\frac{\sqrt{8}}{\sqrt{2}} = \sqrt{\frac{8}{2}} = \sqrt{4} = 2$ . The quotient property works with any positive numbers under the radicals.

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