Solve Square Root Addition: √16 + √4 Step by Step

Q: Can I add the numbers under the square roots first?

No! You cannot combine $ \sqrt{16} + \sqrt{4} $ into $ \sqrt{16 + 4} $. Square roots don't work like that! Always simplify each radical separately first.

Q: What if one of the square roots isn't a perfect square?

If you have something like $ \sqrt{16} + \sqrt{3} $, simplify what you can: $ 4 + \sqrt{3} $. You cannot simplify this further because $ \sqrt{3} $ is irrational.

Q: Why is my calculator giving me a different answer?

Make sure you're entering the problem correctly! Type sqrt(16) + sqrt(4) or use parentheses. If you type sqrt 16 + 4, your calculator might interpret this as $ \sqrt{16} + 4 = 8 $ instead of our correct answer of 6.

Q: Do I need to memorize perfect squares?

Yes! Memorizing perfect squares from 1 to 144 (1² to 12²) will make these problems much faster. Practice with flashcards or write them out daily until they become automatic.

Square Root Evaluation with Perfect Squares

$\sqrt{16}+\sqrt{4}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's solve this question together.

00:07 The square root of a number, N, is equal to N itself.

00:12 We'll use this idea in our problem.

00:16 For example, 16 equals 4 to the power of 2.

00:21 And 4 equals 2 to the power of 2.

00:29 So, the square root of a number, is the number itself.

00:38 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\sqrt{16}+\sqrt{4}=$

Step-by-step solution

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

Step 1: Calculate $\sqrt{16}$ .
Step 2: Calculate $\sqrt{4}$ .
Step 3: Add the results of these operations.

Now, let's work through each step:

Step 1: Calculate the square root of 16.
Since 16 is a perfect square, $\sqrt{16} = 4$ .

Step 2: Calculate the square root of 4.
Since 4 is also a perfect square, $\sqrt{4} = 2$ .

Step 3: Add the results from steps 1 and 2.
Thus, $4 + 2 = 6$ .

Therefore, the solution to the problem is $6$ .

Final Answer

$6$

Key Points to Remember

Essential concepts to master this topic

Rule: Perfect squares have whole number square roots like $\sqrt{16} = 4$
Technique: Simplify each radical first: $\sqrt{16} = 4$ and $\sqrt{4} = 2$
Check: Verify by squaring: $4^2 = 16$ and $2^2 = 4$ , then $4 + 2 = 6$ ✓

Common Mistakes

Avoid these frequent errors

Adding the numbers under the radicals before simplifying
Don't add 16 + 4 = 20 and then find $\sqrt{20}$ ! This gives $\sqrt{20} \approx 4.47$ instead of 6. Radicals don't distribute over addition. Always simplify each square root first, then add the results.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

Can I add the numbers under the square roots first?

No! You cannot combine $\sqrt{16} + \sqrt{4}$ into $\sqrt{16 + 4}$ . Square roots don't work like that! Always simplify each radical separately first.

How do I know if a number is a perfect square?

A perfect square is a whole number that equals another whole number squared. Common perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. If you can think of a whole number that when multiplied by itself gives your number, it's a perfect square!

What if one of the square roots isn't a perfect square?

If you have something like $\sqrt{16} + \sqrt{3}$ , simplify what you can: $4 + \sqrt{3}$ . You cannot simplify this further because $\sqrt{3}$ is irrational.

Why is my calculator giving me a different answer?

Make sure you're entering the problem correctly! Type sqrt(16) + sqrt(4) or use parentheses. If you type sqrt 16 + 4, your calculator might interpret this as $\sqrt{16} + 4 = 8$ instead of our correct answer of 6.

Do I need to memorize perfect squares?

Yes! Memorizing perfect squares from 1 to 144 (1² to 12²) will make these problems much faster. Practice with flashcards or write them out daily until they become automatic.

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Solve Square Root Addition: √16 + √4 Step by Step

Square Root Evaluation with Perfect Squares

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Can I add the numbers under the square roots first?

How do I know if a number is a perfect square?

What if one of the square roots isn't a perfect square?

Why is my calculator giving me a different answer?

Do I need to memorize perfect squares?

🌟 Unlock Your Math Potential

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