Solve: 5 Squared Minus Square Root of 16 Plus 2

Q: Do I calculate 5² or √16 first?

It doesn't matter! Both exponents and radicals have the same priority in order of operations. You can calculate $ 5^2 = 25 $ and $ \sqrt{16} = 4 $ in any order before moving to addition and subtraction.

Q: How do I remember what √16 equals?

Perfect squares are your friend! Remember: $ 4 \times 4 = 16 $, so $ \sqrt{16} = 4 $. Practice memorizing perfect squares 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Q: Why isn't the answer 27?

If you got 27, you likely calculated $ 25 + 4 + 2 $ instead of $ 25 - 4 + 2 $. Remember the subtraction sign in front of the square root: we subtract 4, not add it!

Q: Can I use a calculator for this?

Yes, but be careful with order of operations! Enter it exactly as written or use parentheses. Better yet, practice doing these by hand to build your mental math skills.

Q: What if I get -9 as my answer?

Getting -9 means you probably calculated $ 5^2 $ as 10 instead of 25. Remember: $ 5^2 = 5 \times 5 = 25 $, not $ 5 \times 2 = 10 $!

Order of Operations with Powers and Radicals

$5^2 - \sqrt{16} + 2 =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5^2 - \sqrt{16} + 2 =$

Step-by-step solution

Start by calculating the power: $5^2 = 25$ .

Then, calculate the square root: $\sqrt{16} = 4$ .

Subtract 4 from 25: $25 - 4 = 21$ .

Finally, add 2: $21 + 2 = 23$ .

Final Answer

$23$

Key Points to Remember

Essential concepts to master this topic

Order: Powers and radicals first, then multiplication/division, then addition/subtraction
Technique: Calculate $5^2 = 25$ and $\sqrt{16} = 4$ before combining
Check: Verify: 25 - 4 + 2 = 23 matches the correct answer ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following order of operations
Don't solve 5² - √16 + 2 by doing 5² - √16 first = 25 - 4 = 21, then 21 + 2 = 23. Wait, that's actually correct! The real mistake is calculating √16 incorrectly as 8 instead of 4, giving 25 - 8 + 2 = 19. Always remember √16 = 4, not 8.

Practice Quiz

Test your knowledge with interactive questions

What is the result of the following equation?

$36-4\div2$

FAQ

Everything you need to know about this question

Do I calculate 5² or √16 first?

It doesn't matter! Both exponents and radicals have the same priority in order of operations. You can calculate $5^2 = 25$ and $\sqrt{16} = 4$ in any order before moving to addition and subtraction.

How do I remember what √16 equals?

Perfect squares are your friend! Remember: $4 \times 4 = 16$ , so $\sqrt{16} = 4$ . Practice memorizing perfect squares 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Why isn't the answer 27?

If you got 27, you likely calculated $25 + 4 + 2$ instead of $25 - 4 + 2$ . Remember the subtraction sign in front of the square root: we subtract 4, not add it!

Can I use a calculator for this?

Yes, but be careful with order of operations! Enter it exactly as written or use parentheses. Better yet, practice doing these by hand to build your mental math skills.

What if I get -9 as my answer?

Getting -9 means you probably calculated $5^2$ as 10 instead of 25. Remember: $5^2 = 5 \times 5 = 25$ , not $5 \times 2 = 10$ !

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