Solve (√16 - 2² + 6) ÷ 2²: Order of Operations Challenge

Q: Why can't I just calculate from left to right?

Mathematics has a specific order called PEMDAS to ensure everyone gets the same answer! Without it, $ 2+3 \times 4 $ could equal 20 or 14 - we need rules to avoid confusion.

Q: What's the difference between : and ÷ for division?

Both symbols mean division - they're just different notations! The colon (:) is commonly used in some countries while ÷ is used in others. Both give the same result.

Q: How do I remember to do square roots before addition?

Think of PEMDAS: Parentheses, Exponents (includes square roots), Multiplication/Division, Addition/Subtraction. Square roots are part of the 'E' step!

Q: What if I get a decimal answer - is that wrong?

Decimal answers are perfectly correct! Many math problems result in decimals like 1.5, 2.75, etc. Don't worry - decimals are just another way to express numbers.

Q: Why do we calculate inside parentheses after doing the exponents?

Great question! We do exponents first everywhere, then work inside parentheses. So $ \sqrt{16} $ and $ 2^2 $ become 4, then we calculate $ (4-4+6) $.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 Break down 16 to 4 squared

00:12 The square root of any squared number cancels the square

00:18 Let's use this formula in our exercise

00:28 Calculate the powers

00:40 Always calculate the parentheses first, according to the proper order of operations

00:49 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$(\sqrt{16}-2^2+6):2^2=$

2

Step-by-step solution

Let's solve the expression given in the problem: $(\sqrt{16}-2^2+6):2^2=$

We need to follow the Order of Operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This ensures that we perform calculations in the correct order:

$\sqrt{16}$ simplifies to $4$ because the square root of 16 is 4.
Next, evaluate $2^2$ , which equals $4$ .
Replace these results back into the expression: $(4-4+6):4$ .

Now let's go step-by-step through the simplified expression:

Calculate inside the parentheses: $4 - 4 + 6$ .
$4-4$ equals $0$ .
Then, $0+6$ equals $6$ .
We now have $6:4$ , which denotes division.
Perform the division: $6 \div 4 = 1.5$ .

Thus, the solution to the expression is: $1.5$ .

3

Final Answer

1.5

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Evaluate square roots and exponents before addition and subtraction
Technique: Simplify $\sqrt{16} = 4$ and $2^2 = 4$ first
Check: Substitute back: $(4-4+6) \div 4 = 6 \div 4 = 1.5$ ✓

Common Mistakes

Avoid these frequent errors

Calculating left to right without following order of operations
Don't solve $(\sqrt{16}-2^2+6) \div 2^2$ by going left to right = wrong answer like 0.75! This ignores the proper order and gives incorrect results. Always evaluate square roots and exponents first, then work inside parentheses, then divide.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can't I just calculate from left to right?

+

Mathematics has a specific order called PEMDAS to ensure everyone gets the same answer! Without it, $2+3 \times 4$ could equal 20 or 14 - we need rules to avoid confusion.

What's the difference between : and ÷ for division?

+

Both symbols mean division - they're just different notations! The colon (:) is commonly used in some countries while ÷ is used in others. Both give the same result.

How do I remember to do square roots before addition?

+

Think of PEMDAS: Parentheses, Exponents (includes square roots), Multiplication/Division, Addition/Subtraction. Square roots are part of the 'E' step!

What if I get a decimal answer - is that wrong?

+

Decimal answers are perfectly correct! Many math problems result in decimals like 1.5, 2.75, etc. Don't worry - decimals are just another way to express numbers.

Why do we calculate inside parentheses after doing the exponents?

+

Great question! We do exponents first everywhere, then work inside parentheses. So $\sqrt{16}$ and $2^2$ become 4, then we calculate $(4-4+6)$ .

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Solve (√16 - 2² + 6) ÷ 2²: Order of Operations Challenge

Order of Operations with Square Roots

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