Solve: 8 - Square Root of 16 × 3 | Order of Operations Practice

Q: Why don't I subtract 8 - 4 first?

In the order of operations (PEMDAS/BODMAS), multiplication comes before subtraction. You must calculate $ \sqrt{16} \times 3 $ first, then subtract from 8.

Q: How do I remember the order of operations?

Use PEMDAS (Please Excuse My Dear Aunt Sally) or BODMAS. Both tell you to do multiplication before subtraction, so multiply first, then subtract!

Q: Is √16 always equal to 4?

Yes! The principal square root of 16 is always 4, since $ 4^2 = 16 $. The square root symbol always gives the positive value.

Q: Can the final answer be negative?

Absolutely! When you subtract a larger number from a smaller number, you get negative results. $ 8 - 12 = -4 $ is perfectly correct.

Order of Operations with Square Roots

$8 - \sqrt{16} \times 3 =$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$8 - \sqrt{16} \times 3 =$

Step-by-step solution

First, evaluate the square root: $\sqrt{16}=4$ .

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

1. Multiplication: $4 \times 3 = 12$

2. Subtraction: $8 - 12 = -4$

So, the correct answer is $-4$ .

Final Answer

$-4$

Key Points to Remember

Essential concepts to master this topic

Rule: Evaluate square roots first, then follow PEMDAS/BODMAS order
Technique: Calculate $\sqrt{16} = 4$ , then $4 \times 3 = 12$
Check: Verify final subtraction: $8 - 12 = -4$ matches answer choice ✓

Common Mistakes

Avoid these frequent errors

Subtracting before multiplying
Don't calculate 8 - 4 = 4 first, then multiply by 3 = 12! This ignores the order of operations and gives the wrong answer. Always follow PEMDAS: evaluate square roots and multiplication before subtraction.

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

Why don't I subtract 8 - 4 first?

In the order of operations (PEMDAS/BODMAS), multiplication comes before subtraction. You must calculate $\sqrt{16} \times 3$ first, then subtract from 8.

What if I get a positive answer instead of negative?

A positive answer usually means you subtracted in the wrong order! Remember: $8 - 12 = -4$ (negative), not $12 - 8 = 4$ (positive).

How do I remember the order of operations?

Use PEMDAS (Please Excuse My Dear Aunt Sally) or BODMAS. Both tell you to do multiplication before subtraction, so multiply first, then subtract!

Is √16 always equal to 4?

Yes! The principal square root of 16 is always 4, since $4^2 = 16$ . The square root symbol always gives the positive value.

Can the final answer be negative?

Absolutely! When you subtract a larger number from a smaller number, you get negative results. $8 - 12 = -4$ is perfectly correct.

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