What is (a+b+c) Whole Square?

S3-SA1-0049

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The expression (a+b+c) whole square means multiplying the sum of three numbers (a, b, and c) by itself. It's written as (a+b+c)^2. This concept helps us quickly expand and simplify expressions involving three terms added together and then squared.

Simple Example

Quick Example

Imagine you have three friends, Rohan, Priya, and Sameer. Rohan has 2 cricket bats, Priya has 3, and Sameer has 1. If you want to know the 'square' of their total bats, you would calculate (2+3+1)^2. First, add them up: 2+3+1 = 6. Then, square the total: 6^2 = 36.

Worked Example

Step-by-Step

Let's find the value of (2+3+4) whole square.
1. First, identify the values of a, b, and c. Here, a=2, b=3, c=4.
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2. Add the numbers inside the bracket: 2 + 3 + 4 = 9.
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3. Now, square the sum: 9^2.
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4. This means multiplying 9 by itself: 9 * 9.
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5. Calculate the product: 9 * 9 = 81.
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So, (2+3+4) whole square is 81.

Why It Matters

Understanding (a+b+c) whole square helps solve problems faster in subjects like Physics for calculating areas or volumes, and in Computer Science for optimizing code. Engineers use this concept when designing structures or circuits, making sure everything fits perfectly and works efficiently.

Common Mistakes

MISTAKE: Squaring each term separately and adding them: (a^2 + b^2 + c^2) | CORRECTION: Remember to add the terms first, then square the sum: (a+b+c)^2. The square applies to the entire sum, not individual terms.

MISTAKE: Forgetting the brackets and just squaring the last term: a+b+c^2 | CORRECTION: The 'whole square' means the entire expression (a+b+c) is multiplied by itself. Always keep the brackets in mind.

MISTAKE: Confusing (a+b+c)^2 with (a+b+c) * 2 | CORRECTION: Squaring means multiplying a number or expression by itself, not by 2. (a+b+c)^2 means (a+b+c) * (a+b+c).

Practice Questions

Try It Yourself

QUESTION: What is the value of (1+2+3) whole square? | ANSWER: 36

QUESTION: If a=5, b=2, and c=3, find (a+b+c) whole square. | ANSWER: 100

QUESTION: A rectangular garden has sides of length 'x', 'y', and 'z' meters. If you want to find the square of the sum of these lengths, and x=10, y=5, z=5, what is the result? | ANSWER: 400

MCQ

Quick Quiz

Which of these correctly represents (5+2+3) whole square?

(5*5) + (2*2) + (3*3)

5 + 2 + (3*3)

(5+2+3) * (5+2+3)

(5+2+3) * 2

The Correct Answer Is:

Option C correctly shows that 'whole square' means multiplying the entire sum (5+2+3) by itself. Options A, B, and D show incorrect ways of calculating a whole square.

Real World Connection

In the Real World

Imagine an architect designing a new building in Mumbai. They might need to calculate the total length of three different sections of a wall, say 'A', 'B', and 'C', and then use (A+B+C) whole square in formulas to determine the total material needed or the stress on certain points. This ensures the building is strong and safe.

Key Vocabulary

Key Terms

SQUARE: Multiplying a number or expression by itself | EXPRESSION: A combination of numbers, variables, and operation symbols | TERM: A single number or variable, or product of numbers and variables | SUM: The result of adding two or more numbers | BRACKETS: Symbols like () used to group parts of an expression

What's Next

What to Learn Next

Great job understanding (a+b+c) whole square! Next, you can explore the algebraic expansion of (a+b+c)^2, which gives a formula like a^2+b^2+c^2+2ab+2bc+2ca. This will help you solve problems even faster without first adding the numbers.