Solve Square Root: Evaluate √(196/4) Step by Step

Q: Why do I need to simplify the fraction first?

Simplifying makes the calculation easier! It's much simpler to find $ \sqrt{49} = 7 $ than to work with $ \sqrt{\frac{196}{4}} $ directly.

Q: Can I use the property that square root of a fraction equals fraction of square roots?

Yes, $ \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} $ is a valid property! However, simplifying first is usually faster and less prone to calculation errors.

Q: How do I know if 196 ÷ 4 equals 49?

Use long division or think: 4 × 49 = 196. You can also break it down: $ 4 \times 50 = 200 $, so $ 4 \times 49 = 196 $.

Q: What's the fastest way to recognize that √49 = 7?

Memorize perfect squares! Know that $ 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2=100 $. This makes square root problems much faster!

Square Root Operations with Fraction Simplification

Complete the following exercise:

$\sqrt{\frac{196}{4}}=$

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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 a 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

00:18 Break down 196 to 14 squared

00:22 Break down 4 to 2 squared

00:25 The root of any number (A) squared cancels out the square

00:32 Apply this formula to our exercise

00:37 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:

$\sqrt{\frac{196}{4}}=$

Step-by-step solution

To solve the problem $\sqrt{\frac{196}{4}}$ , we can apply the following steps:

Step 1: Simplify the fraction $\frac{196}{4}$ .
Step 2: Compute the square root of the result from Step 1.

Let's go through these steps in detail:

Step 1: Simplify the fraction.

The fraction $\frac{196}{4}$ can be simplified by dividing 196 by 4.

$\frac{196}{4} = 49$

Step 2: Take the square root of 49.

$\sqrt{49} = 7$ because $7 \times 7 = 49$ .

Therefore, the solution to the problem is $\boxed{7}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Simplify the fraction inside the radical before taking square root
Technique: Divide numerator by denominator: $\frac{196}{4} = 49$ , then $\sqrt{49} = 7$
Check: Verify that $7^2 = 49$ and $49 \times 4 = 196$ ✓

Common Mistakes

Avoid these frequent errors

Taking square root of numerator and denominator separately
Don't calculate $\frac{\sqrt{196}}{\sqrt{4}} = \frac{14}{2} = 7$ using separate square roots! This happens to work but creates bad habits and confusion. Always simplify the fraction first, then take one square root: $\sqrt{\frac{196}{4}} = \sqrt{49} = 7$ .

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 do I need to simplify the fraction first?

Simplifying makes the calculation easier! It's much simpler to find $\sqrt{49} = 7$ than to work with $\sqrt{\frac{196}{4}}$ directly.

Can I use the property that square root of a fraction equals fraction of square roots?

Yes, $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ is a valid property! However, simplifying first is usually faster and less prone to calculation errors.

What if the fraction doesn't simplify to a perfect square?

If the simplified fraction isn't a perfect square, leave your answer as $\sqrt{\text{simplified fraction}}$ . For example, $\sqrt{\frac{50}{2}} = \sqrt{25} = 5$ , but $\sqrt{\frac{48}{3}} = \sqrt{16} = 4$ .

How do I know if 196 ÷ 4 equals 49?

Use long division or think: 4 × 49 = 196. You can also break it down: $4 \times 50 = 200$ , so $4 \times 49 = 196$ .

What's the fastest way to recognize that √49 = 7?

Memorize perfect squares! Know that $1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2=100$ . This makes square root problems much faster!

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