Solve: 7 + √49 - 5 | Square Root and Basic Operations

Q: How do I know what √49 equals?

Think: what number times itself gives 49? Since $ 7 \times 7 = 49 $, we know $ \sqrt{49} = 7 $. Perfect squares like 1, 4, 9, 16, 25, 36, 49 are great to memorize!

Q: Do I add first or find the square root first?

Always evaluate the square root first! Square roots are like parentheses - they group the number underneath. So $ \sqrt{49} $ becomes 7 before you do any adding or subtracting.

Q: Why don't I get 11 as the answer?

If you got 11, you probably calculated $ 7 + 7 - 5 + 2 $ somehow. Remember: $ \sqrt{49} = 7 $ exactly, so the expression is just $ 7 + 7 - 5 = 9 $.

Q: Can I leave the answer as 2 + √49?

The question asks you to solve the expression, which means find the final numerical value. Since $ \sqrt{49} = 7 $ is a perfect square, you should simplify completely to get 9.

Q: What if I don't remember that √49 = 7?

You can figure it out! Try small numbers: $ 6 \times 6 = 36 $ (too small), $ 8 \times 8 = 64 $ (too big), so $ 7 \times 7 = 49 $ must be right!

Square Root Evaluation with Mixed Operations

$7 + \sqrt{49} - 5 =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$7 + \sqrt{49} - 5 =$

Step-by-step solution

First, evaluate the square root: $\sqrt{49}=7$ .

Then, follow the order of operations (PEMDAS/BODMAS):

1. Addition: $7 + 7 = 14$

2. Subtraction: $14 - 5 = 9$

So, the correct answer is $9$ .

Final Answer

$9$

Key Points to Remember

Essential concepts to master this topic

Square Roots: $\sqrt{49} = 7$ because $7 \times 7 = 49$
Order of Operations: Calculate $7 + 7 = 14$ , then $14 - 5 = 9$
Verification: Check by working backwards: $9 + 5 = 14$ and $14 - 7 = 7$ ✓

Common Mistakes

Avoid these frequent errors

Adding and subtracting before evaluating the square root
Don't calculate 7 + 49 - 5 = 51 first, then try to take the square root! This completely changes the expression and gives $\sqrt{51} \approx 7.14$ instead of 9. Always evaluate square roots first, then follow left-to-right operations.

Practice Quiz

Test your knowledge with interactive questions

$5+\sqrt{36}-1=$

FAQ

Everything you need to know about this question

How do I know what √49 equals?

Think: what number times itself gives 49? Since $7 \times 7 = 49$ , we know $\sqrt{49} = 7$ . Perfect squares like 1, 4, 9, 16, 25, 36, 49 are great to memorize!

Do I add first or find the square root first?

Always evaluate the square root first! Square roots are like parentheses - they group the number underneath. So $\sqrt{49}$ becomes 7 before you do any adding or subtracting.

Why don't I get 11 as the answer?

If you got 11, you probably calculated $7 + 7 - 5 + 2$ somehow. Remember: $\sqrt{49} = 7$ exactly, so the expression is just $7 + 7 - 5 = 9$ .

Can I leave the answer as 2 + √49?

The question asks you to solve the expression, which means find the final numerical value. Since $\sqrt{49} = 7$ is a perfect square, you should simplify completely to get 9.

What if I don't remember that √49 = 7?

You can figure it out! Try small numbers: $6 \times 6 = 36$ (too small), $8 \times 8 = 64$ (too big), so $7 \times 7 = 49$ must be right!

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