Solve √49 + √36: Adding Square Roots of Perfect Squares

Q: Why can't I add 49 + 36 first and then take the square root?

Because √49 + √36 is completely different from √(49 + 36)! The first means "find each square root, then add" while the second means "add first, then find the square root." Always follow order of operations!

Q: How do I quickly recognize perfect squares?

Memorize the first 12 perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. These come from $ 1^2 $ through $ 12^2 $. Practice until you know them instantly!

Q: What if I don't recognize a perfect square immediately?

Try factoring! Look for patterns like 49 = 7 × 7 or think "what number times itself gives me 49?" You can also work backwards from numbers you know.

Q: Do I need to simplify √49 + √36 any further after getting 13?

No! Once you've calculated 7 + 6 = 13, you're done. The answer 13 is already in its simplest form since it's a whole number.

Q: Can square roots of perfect squares ever be negative?

In basic math, we always use the principal (positive) square root. So $ \sqrt{49} = 7 $, not -7, even though both 7 and -7 when squared equal 49.

Square Roots with Perfect Square Recognition

$\sqrt{49}+\sqrt{36}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 The square root of any number (N) squared, root cancels square

00:07 We will use this formula in our exercise

00:11 We'll break down 49 to 7 squared

00:19 We'll break down 36 to 6 squared

00:26 Root and square cancel out

00:32 Let's calculate and solve

00:35 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\sqrt{49}+\sqrt{36}=$

Step-by-step solution

To solve this problem, we will find the square roots of the given numbers and add the results:

First, compute $\sqrt{49}$ . Since $7^2 = 49$ , we have $\sqrt{49} = 7$ .
Next, compute $\sqrt{36}$ . Since $6^2 = 36$ , we have $\sqrt{36} = 6$ .
The final step is to sum these square roots: $7 + 6 = 13$ .

Therefore, the solution to the problem is $13$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Perfect squares have whole number square roots
Technique: Recognize that $7^2 = 49$ and $6^2 = 36$
Check: Verify $7^2 + 6^2 = 49 + 36 = 85$ but answer is 13 ✓

Common Mistakes

Avoid these frequent errors

Adding under the radical sign first
Don't calculate √(49 + 36) = √85 ≈ 9.2! This treats the expression as one radical instead of two separate ones. Always find each square root individually first, then add: √49 + √36 = 7 + 6 = 13.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

Why can't I add 49 + 36 first and then take the square root?

Because √49 + √36 is completely different from √(49 + 36)! The first means "find each square root, then add" while the second means "add first, then find the square root." Always follow order of operations!

How do I quickly recognize perfect squares?

Memorize the first 12 perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. These come from $1^2$ through $12^2$ . Practice until you know them instantly!

What if I don't recognize a perfect square immediately?

Try factoring! Look for patterns like 49 = 7 × 7 or think "what number times itself gives me 49?" You can also work backwards from numbers you know.

Do I need to simplify √49 + √36 any further after getting 13?

No! Once you've calculated 7 + 6 = 13, you're done. The answer 13 is already in its simplest form since it's a whole number.

Can square roots of perfect squares ever be negative?

In basic math, we always use the principal (positive) square root. So $\sqrt{49} = 7$ , not -7, even though both 7 and -7 when squared equal 49.

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