Simplify the Square Root: √(196/49) Step-by-Step Solution

Q: How do I remember which numbers are perfect squares?

Practice the squares from 1 to 15: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. Notice that 196 = 14² and 49 = 7²!

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

You can still use the quotient property! For example: $ \sqrt{\frac{18}{2}} = \frac{\sqrt{18}}{\sqrt{2}} = \frac{3\sqrt{2}}{\sqrt{2}} = 3 $. Break down any non-perfect squares into simpler radicals.

Q: Can I simplify the fraction before taking the square root?

Yes! If $ \frac{196}{49} $ simplifies to $ \frac{4 \times 49}{49} = 4 $, then $ \sqrt{4} = 2 $. Both methods give the same answer!

Q: How do I check my answer is correct?

Square your answer and compare: $ 2^2 = 4 $, and $ \frac{196}{49} = \frac{14^2}{7^2} = \left(\frac{14}{7}\right)^2 = 2^2 = 4 $ ✓

Square Root Simplification with Fractional Radicands

Complete the following exercise:

$\sqrt{\frac{196}{49}}=$

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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 The root of the fraction (A divided by B)

00:07 Equals the root of the numerator (A) divided by the root of the denominator (B)

00:11 Apply this formula to our exercise

00:19 Factorize 196 into 14 squared

00:24 Factorize 19 into 7 squared

00:29 The root of any number (A) squared cancels out the square

00:32 Apply this formula to our exercise and proceed to cancel out the squares

00:41 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following exercise:

$\sqrt{\frac{196}{49}}=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Apply the square root quotient property.
Step 2: Calculate the square roots of the numerator and the denominator.
Step 3: Simplify the resulting expression.

Now, let's work through each step:
Step 1: Apply the square root quotient property $\sqrt{\frac{196}{49}} = \frac{\sqrt{196}}{\sqrt{49}}$ .
Step 2: Calculate the individual square roots: $\sqrt{196} = 14$ and $\sqrt{49} = 7$ .
Step 3: Simplify the expression to $\frac{14}{7} = 2$ .

Therefore, the solution to the problem is 2.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Quotient Property: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ separates numerator and denominator
Perfect Squares: Identify $\sqrt{196} = 14$ and $\sqrt{49} = 7$
Verify: Check that $2^2 = 4$ and $\frac{196}{49} = 4$ ✓

Common Mistakes

Avoid these frequent errors

Taking square root of fraction as a whole
Don't calculate $\sqrt{196/49}$ by first dividing 196 ÷ 49 = 4, then $\sqrt{4} = 2$ ! While this gives the right answer here, it creates confusion and won't work with non-perfect square quotients. Always use the quotient property to separate the square roots 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

Why can't I just divide 196 by 49 first, then take the square root?

While this works when the quotient is a perfect square (like 4), it won't work for problems like $\sqrt{\frac{50}{8}}$ . Using the quotient property is the reliable method that works every time!

How do I remember which numbers are perfect squares?

Practice the squares from 1 to 15: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. Notice that 196 = 14² and 49 = 7²!

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

You can still use the quotient property! For example: $\sqrt{\frac{18}{2}} = \frac{\sqrt{18}}{\sqrt{2}} = \frac{3\sqrt{2}}{\sqrt{2}} = 3$ . Break down any non-perfect squares into simpler radicals.

Can I simplify the fraction before taking the square root?

Yes! If $\frac{196}{49}$ simplifies to $\frac{4 \times 49}{49} = 4$ , then $\sqrt{4} = 2$ . Both methods give the same answer!

How do I check my answer is correct?

Square your answer and compare: $2^2 = 4$ , and $\frac{196}{49} = \frac{14^2}{7^2} = \left(\frac{14}{7}\right)^2 = 2^2 = 4$ ✓

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