Solve 5² - 4² + 2²: Perfect Square Operations Practice

Q: Do I really need to calculate each square separately?

Yes! You cannot combine the squares before calculating them. $ 5^2 - 4^2 $ is NOT the same as $ (5-4)^2 $. Each exponent must be calculated individually first.

Q: Why do I subtract before adding when both have the same priority?

When operations have equal priority (like addition and subtraction), work from left to right. So $ 25 - 16 + 4 $ becomes $ 9 + 4 = 13 $, not $ 25 - 20 = 5 $.

Q: What's the easiest way to remember perfect squares?

Practice the first 10 perfect squares: $ 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25 $, etc. These appear frequently and knowing them by heart saves time!

Q: Can I use a calculator for the squares?

While calculators are helpful, try to memorize common squares like $ 2^2, 3^2, 4^2, 5^2 $. This builds number sense and makes mental math much faster!

Perfect Square Operations with Order of Operations

Solve the following exercise and circle the correct answer:

$5^2-4^2+2^2=$

❤️ Continue Your Math Journey!

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

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:05 Let's break down the exponents

00:27 Always solve multiplication and division before addition and subtraction

00:47 Continue to solve the expression from left to right, one operation at a time

00:54 This is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise and circle the correct answer:

$5^2-4^2+2^2=$

Step-by-step solution

To solve the expression $5^2 - 4^2 + 2^2$ , we'll need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here, we only have exponents and basic arithmetic.

First, calculate the powers:
$5^2 = 25$ ,
$4^2 = 16$ ,
$2^2 = 4$ .

Now substitute the calculated values back into the expression:
$25 - 16 + 4$ .

Perform the subtraction and addition from left to right:
$25 - 16 = 9$ .

Then add $4$ to $9$ :
$9 + 4 = 13$ .

The final answer is $13$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Calculate all exponents first, then addition and subtraction left to right
Technique: $5^2 = 25$ , $4^2 = 16$ , $2^2 = 4$ , then evaluate 25 - 16 + 4
Check: Verify by substituting: $25 - 16 + 4 = 9 + 4 = 13$ ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting before calculating exponents
Don't try to combine 5² - 4² as (5-4)² = 1! This ignores order of operations and gives 1 + 4 = 5 instead of 13. Always calculate each exponent separately first, then perform addition and subtraction from left to right.

Practice Quiz

Test your knowledge with interactive questions

$$ 100+5-100+5 $$

FAQ

Everything you need to know about this question

Do I really need to calculate each square separately?

Yes! You cannot combine the squares before calculating them. $5^2 - 4^2$ is NOT the same as $(5-4)^2$ . Each exponent must be calculated individually first.

Why do I subtract before adding when both have the same priority?

When operations have equal priority (like addition and subtraction), work from left to right. So $25 - 16 + 4$ becomes $9 + 4 = 13$ , not $25 - 20 = 5$ .

What's the easiest way to remember perfect squares?

Practice the first 10 perfect squares: $1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25$ , etc. These appear frequently and knowing them by heart saves time!

Can I use a calculator for the squares?

While calculators are helpful, try to memorize common squares like $2^2, 3^2, 4^2, 5^2$ . This builds number sense and makes mental math much faster!

What if I get a different answer than the choices given?

Double-check your work! Make sure you calculated each square correctly and followed left-to-right order for addition/subtraction. Recompute step by step to find where the error occurred.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Powers and Roots - Basic 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

Solve 5² - 4² + 2²: Perfect Square Operations Practice

Perfect Square Operations with Order of Operations

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Do I really need to calculate each square separately?

Why do I subtract before adding when both have the same priority?

What's the easiest way to remember perfect squares?

Can I use a calculator for the squares?

What if I get a different answer than the choices given?

🌟 Unlock Your Math Potential

More Questions

Powers and Roots

Solve the Expression: 4² - 4³ (Exponent Subtraction)

Solve 6³ - 6²: Calculating the Difference Between Cube and Square Powers

Solve (18-10)² + 3³: Combined Square and Cube Number Problem

Solve (4²:8):2+3²: Order of Operations Practice

Powers

Solve the Expression: Finding 7^1 - 7^2

Solve 5² minus 4¹: Basic Exponent Calculation

Solve 3-(5²÷5)²+7²: Order of Operations Challenge

Calculate Square Area: Finding Area When Side Length is 8 Units

All Operations in the Order of Operations

Solve 5 + (4/7 ÷ 2): Complex Fraction Addition Problem

Solve the Fraction: Finding the Value of 18/(18+36)

Solve 4² ÷ 2 + 5²: Order of Operations Practice

Solve 2^4 - 4:2^2: Order of Operations with Exponents