What is a Root of an Equation?

S3-SA1-0014

Grade Level:

Class 6

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

Definition

What is it?

A 'root' of an equation is simply the value that makes the equation true. When you put this special number into the equation, both sides become equal, like a perfectly balanced weighing scale.

Simple Example

Quick Example

Imagine you have a puzzle: 'My age plus 5 years is 17 years.' What is my age? Here, 'my age' is the unknown. The number that makes this statement true (12, because 12 + 5 = 17) is the root of this age puzzle.

Worked Example

Step-by-Step

Let's find the root of the equation: x + 7 = 15

1. Our goal is to find the value of 'x' that makes the equation true.
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2. To get 'x' by itself on one side, we need to remove the '+ 7'.
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3. We do the opposite operation: subtract 7 from both sides of the equation. This keeps the equation balanced.
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4. So, x + 7 - 7 = 15 - 7
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5. This simplifies to x = 8.
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6. To check, substitute x = 8 back into the original equation: 8 + 7 = 15. Since 15 = 15, our answer is correct.
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ANSWER: The root of the equation x + 7 = 15 is x = 8.

Why It Matters

Understanding roots helps you solve problems in science, engineering, and even predict future trends! Data scientists use roots to understand patterns, and engineers use them to design everything from bridges to rockets. It's a key step in becoming a problem-solver in many exciting careers.

Common Mistakes

MISTAKE: Adding or subtracting only from one side of the equation. | CORRECTION: Always perform the same operation (add, subtract, multiply, divide) on BOTH sides of the equation to keep it balanced.

MISTAKE: Confusing the root with the answer to a multiplication or division problem when it should be addition or subtraction. | CORRECTION: Identify the operation next to the unknown variable and perform its opposite to isolate the variable.

MISTAKE: Not checking the answer by substituting the found root back into the original equation. | CORRECTION: Always substitute your found root back into the original equation to verify if it makes the equation true.

Practice Questions

Try It Yourself

QUESTION: Find the root of the equation: y - 3 = 10 | ANSWER: y = 13

QUESTION: What is the root of the equation: 2 * z = 18 (Hint: '*' means multiply) | ANSWER: z = 9

QUESTION: A chaiwallah sold 'p' cups of chai. If he sold 5 more cups, he would have sold 20 cups in total. Write an equation and find the root for 'p'. | ANSWER: Equation: p + 5 = 20. Root: p = 15.

MCQ

Quick Quiz

Which of these is the root of the equation: x + 9 = 14?

The Correct Answer Is:

If x = 5, then 5 + 9 = 14, which makes the equation true. Options A, C, and D do not satisfy the equation.

Real World Connection

In the Real World

When you use a GPS app like Google Maps or Ola to find the shortest route, the app's algorithms are solving equations to find the 'root' – which is the optimal path or travel time. Similarly, when ISRO scientists launch rockets, they solve complex equations to find the exact 'roots' (values) for fuel, speed, and direction to reach their target.

Key Vocabulary

Key Terms

EQUATION: A mathematical statement showing two expressions are equal. | VARIABLE: A symbol (like x, y, z) that represents an unknown value. | SOLVE: To find the value of the variable that makes the equation true. | BALANCE: Keeping both sides of an equation equal.

What's Next

What to Learn Next

Great job understanding roots! Now you're ready to learn about 'Linear Equations in One Variable'. This will help you solve even more interesting puzzles and real-life problems where you need to find an unknown value.