Solve 3 × 2 + √81: Order of Operations with Square Root

Q: Why do I calculate the square root first?

Square roots are considered exponents in PEMDAS, so they come before multiplication and addition. Think of $ \sqrt{81} $ as $ 81^{1/2} $ - exponents always go first!

Q: What if I forgot PEMDAS and added first?

You'd get the wrong answer! If you do $ 2 + 9 = 11 $ first, then $ 3 \times 11 = 33 $, you get 33 instead of 15. Always follow the order of operations.

Q: How do I remember the order of operations?

Use PEMDAS: Parentheses, Exponents (including square roots), Multiplication and Division (left to right), Addition and Subtraction (left to right). Some students remember it as "Please Excuse My Dear Aunt Sally."

Q: What if the square root wasn't a perfect square?

If $ \sqrt{81} $ were something like $ \sqrt{80} $, you'd still evaluate it first in the order of operations. You might need to approximate or leave it in radical form, but it still comes before multiplication and addition.

Order of Operations with Square Roots

$3 \times 2 + \sqrt{81} =$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$3 \times 2 + \sqrt{81} =$

Step-by-step solution

First, evaluate the square root: $\sqrt{81}=9$ .

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

1. Multiplication: $3 \times 2 = 6$

2. Addition: $6 + 9 = 15$

So, the correct answer is $15$ .

Final Answer

$15$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Always evaluate square roots before multiplication and addition
Technique: Calculate $\sqrt{81} = 9$ , then $3 \times 2 = 6$ , finally $6 + 9 = 15$
Check: Verify each step matches PEMDAS order: square root first, multiplication second, addition last ✓

Common Mistakes

Avoid these frequent errors

Adding before multiplying
Don't calculate 2 + 9 = 11 first, then multiply 3 × 11 = 33! This ignores the order of operations and gives 33 instead of 15. Always follow PEMDAS: do multiplication before addition, even when addition appears first in the expression.

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 do I calculate the square root first?

Square roots are considered exponents in PEMDAS, so they come before multiplication and addition. Think of $\sqrt{81}$ as $81^{1/2}$ - exponents always go first!

What if I forgot PEMDAS and added first?

You'd get the wrong answer! If you do $2 + 9 = 11$ first, then $3 \times 11 = 33$ , you get 33 instead of 15. Always follow the order of operations.

How do I remember the order of operations?

Use PEMDAS: Parentheses, Exponents (including square roots), Multiplication and Division (left to right), Addition and Subtraction (left to right). Some students remember it as "Please Excuse My Dear Aunt Sally."

Are there parentheses in this problem?

No, this problem has no parentheses. We start with the E in PEMDAS - the square root $\sqrt{81}$ , then move to M for multiplication, and finally A for addition.

What if the square root wasn't a perfect square?

If $\sqrt{81}$ were something like $\sqrt{80}$ , you'd still evaluate it first in the order of operations. You might need to approximate or leave it in radical form, but it still comes before multiplication and addition.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 The Order of Operations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime