Evaluate (4² + 3) × √9: Order of Operations Practice

Q: Why do I need to calculate the exponent before adding 3?

According to PEMDAS, exponents come before addition! You must calculate $ 4^2 = 16 $ first, then add 3 to get 19 inside the parentheses.

Q: Can I multiply 4 by the square root first?

No! The parentheses group $ (4^2 + 3) $ together as one unit. You must completely solve what's inside the parentheses first before multiplying by $ \sqrt{9} $.

Q: What if I forget that √9 equals 3?

Remember that $ \sqrt{9} = 3 $ because $ 3 \times 3 = 9 $. Practice your perfect square roots: $ \sqrt{1} = 1 $, $ \sqrt{4} = 2 $, $ \sqrt{9} = 3 $, $ \sqrt{16} = 4 $, etc.

Q: How can I remember the order of operations?

Use the memory device PEMDAS: "Please Excuse My Dear Aunt Sally" for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Work left to right within each level!

Q: What happens if I get 25 as my answer?

Getting 25 means you probably calculated $ (4^2 + 3) + \sqrt{9} = 16 + 3 + 3 = 22 $ instead of multiplying. Remember the × symbol means multiplication, not addition!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this problem together!

00:09 First, calculate 4 squared. That means 4 times 4.

00:17 Remember, always do the parentheses first.

00:24 Let's break down 9 into 3 squared. So, 3 times 3.

00:30 Square root cancels out a square number.

00:35 We'll apply this formula in our exercise.

00:44 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$(4^2+3)\times\sqrt{9}=$

2

Step-by-step solution

To solve the expression $(4^2+3)\times\sqrt{9}=$ , we need to follow the order of operations, also known as PEMDAS/BODMAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

First, we deal with the exponent $4^2$ , which means 4 raised to the power of 2. Calculate $4^2 = 16$ .
Next, we calculate the expression inside the parentheses: $(4^2+3)$ . We already know $4^2 = 16$ , so we add 3 to 16: $16 + 3 = 19$ .
Then, we find the square root of 9: $\sqrt{9} = 3$ .
Lastly, we perform the multiplication: $19 \times 3 = 57$ .

Thus, the final result of the expression $(4^2+3)\times\sqrt{9}$ is 57.

3

Final Answer

57

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Work through parentheses, exponents, multiplication, division, addition, subtraction in order
Technique: Calculate $4^2 = 16$ first, then $16 + 3 = 19$ inside parentheses
Check: Final multiplication $19 \times 3 = 57$ gives the correct answer ✓

Common Mistakes

Avoid these frequent errors

Ignoring the order of operations and working left to right
Don't calculate $(4^2 + 3) \times \sqrt{9}$ as 4 × 2 + 3 × 3 = 17! This skips exponents and radicals. Always follow PEMDAS: calculate $4^2 = 16$ first, then $(16 + 3) = 19$ , then $\sqrt{9} = 3$ , finally $19 \times 3 = 57$ .

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 need to calculate the exponent before adding 3?

+

According to PEMDAS, exponents come before addition! You must calculate $4^2 = 16$ first, then add 3 to get 19 inside the parentheses.

Can I multiply 4 by the square root first?

+

No! The parentheses group $(4^2 + 3)$ together as one unit. You must completely solve what's inside the parentheses first before multiplying by $\sqrt{9}$ .

What if I forget that √9 equals 3?

+

Remember that $\sqrt{9} = 3$ because $3 \times 3 = 9$ . Practice your perfect square roots: $\sqrt{1} = 1$ , $\sqrt{4} = 2$ , $\sqrt{9} = 3$ , $\sqrt{16} = 4$ , etc.

How can I remember the order of operations?

+

Use the memory device PEMDAS: "Please Excuse My Dear Aunt Sally" for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Work left to right within each level!

What happens if I get 25 as my answer?

+

Getting 25 means you probably calculated $(4^2 + 3) + \sqrt{9} = 16 + 3 + 3 = 22$ instead of multiplying. Remember the × symbol means multiplication, not addition!

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Evaluate (4² + 3) × √9: Order of Operations Practice

Order of Operations with Exponents and Radicals

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