Solve The Equation:${ (2)^2 = \sqrt{\left(\frac{p}{6}\right)^2} }$

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Introduction

In this article, we will delve into the world of mathematics and solve a simple yet intriguing equation. The equation in question is: (2)2=(p6)2(2)^2 = \sqrt{\left(\frac{p}{6}\right)^2}. We will break down the solution step by step, making it easy to follow and understand for readers of all levels.

Understanding the Equation

Before we dive into the solution, let's take a closer look at the equation. The equation consists of two parts: the left-hand side and the right-hand side. The left-hand side is a simple squared expression, while the right-hand side is a square root expression.

The left-hand side of the equation is (2)2(2)^2, which is equal to 44. This is a basic algebraic expression that can be evaluated easily.

The right-hand side of the equation is (p6)2\sqrt{\left(\frac{p}{6}\right)^2}. This expression involves a square root and a fraction. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we are taking the square root of the squared fraction (p6)2\left(\frac{p}{6}\right)^2.

Simplifying the Right-Hand Side

To simplify the right-hand side of the equation, we need to evaluate the expression inside the square root. The expression is (p6)2\left(\frac{p}{6}\right)^2, which can be rewritten as p236\frac{p^2}{36}.

Now, we can take the square root of this expression. The square root of p236\frac{p^2}{36} is p6\frac{p}{6}.

Equating the Left-Hand Side and the Right-Hand Side

Now that we have simplified the right-hand side of the equation, we can equate it to the left-hand side. The equation becomes:

4=p64 = \frac{p}{6}

Solving for p

To solve for p, we need to isolate p on one side of the equation. We can do this by multiplying both sides of the equation by 6.

24=p24 = p

Conclusion

In this article, we solved the equation (2)2=(p6)2(2)^2 = \sqrt{\left(\frac{p}{6}\right)^2}. We broke down the solution step by step, making it easy to follow and understand for readers of all levels. We simplified the right-hand side of the equation, equated it to the left-hand side, and solved for p.

Final Answer

The final answer to the equation is p=24p = 24.

Related Topics

  • Algebraic expressions
  • Square roots
  • Fractions
  • Equations

Further Reading

If you want to learn more about algebraic expressions, square roots, fractions, and equations, check out the following resources:

  • Khan Academy: Algebra
  • Mathway: Algebra Solver
  • Wolfram Alpha: Algebra Calculator

References

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Introduction

In our previous article, we solved the equation (2)2=(p6)2(2)^2 = \sqrt{\left(\frac{p}{6}\right)^2}. We broke down the solution step by step, making it easy to follow and understand for readers of all levels. In this article, we will answer some frequently asked questions related to the equation and its solution.

Q&A

Q: What is the final answer to the equation?

A: The final answer to the equation is p=24p = 24.

Q: How do I simplify the right-hand side of the equation?

A: To simplify the right-hand side of the equation, you need to evaluate the expression inside the square root. The expression is (p6)2\left(\frac{p}{6}\right)^2, which can be rewritten as p236\frac{p^2}{36}. Then, you can take the square root of this expression, which is p6\frac{p}{6}.

Q: How do I equate the left-hand side and the right-hand side of the equation?

A: To equate the left-hand side and the right-hand side of the equation, you need to set them equal to each other. The equation becomes:

4=p64 = \frac{p}{6}

Q: How do I solve for p?

A: To solve for p, you need to isolate p on one side of the equation. You can do this by multiplying both sides of the equation by 6.

24=p24 = p

Q: What is the difference between the left-hand side and the right-hand side of the equation?

A: The left-hand side of the equation is a simple squared expression, while the right-hand side is a square root expression. The left-hand side is equal to 44, while the right-hand side is equal to p6\frac{p}{6}.

Q: How do I use algebraic expressions to solve the equation?

A: Algebraic expressions are used to represent unknown values or variables. In this equation, the variable is p. To solve the equation, you need to use algebraic expressions to isolate p on one side of the equation.

Q: What is the importance of square roots in solving the equation?

A: Square roots are used to find the value of an expression that is raised to a power. In this equation, the square root is used to find the value of p6\frac{p}{6}.

Q: How do I use fractions to solve the equation?

A: Fractions are used to represent part of a whole. In this equation, the fraction p6\frac{p}{6} is used to represent the value of p.

Conclusion

In this article, we answered some frequently asked questions related to the equation and its solution. We covered topics such as simplifying the right-hand side of the equation, equating the left-hand side and the right-hand side of the equation, solving for p, and using algebraic expressions, square roots, and fractions to solve the equation.

Final Answer

The final answer to the equation is p=24p = 24.

Related Topics

  • Algebraic expressions
  • Square roots
  • Fractions
  • Equations

Further Reading

If you want to learn more about algebraic expressions, square roots, fractions, and equations, check out the following resources:

  • Khan Academy: Algebra
  • Mathway: Algebra Solver
  • Wolfram Alpha: Algebra Calculator

References