Solve For $t$. 68 T = 68 68 \sqrt{t} = 68 68 T ​ = 68 T = T = T =

Solving for Time: A Step-by-Step Guide to Isolate t in the Equation $68 \sqrt{t} = 68t$

In mathematics, solving for a variable is a crucial concept that helps us understand the relationship between different quantities. In this article, we will focus on solving for time, denoted by the variable $t$, in the equation $68 \sqrt{t} = 68t$. This equation involves a square root, which can be challenging to solve. However, with a step-by-step approach, we can isolate $t$ and find its value.

Understanding the Equation

The given equation is $68 \sqrt{t} = 68t$. To solve for $t$, we need to isolate it on one side of the equation. The equation involves a square root, which can be simplified by squaring both sides of the equation.

Squaring Both Sides

To eliminate the square root, we can square both sides of the equation. This will help us get rid of the square root and make it easier to solve for $t$. Squaring both sides of the equation $68 \sqrt{t} = 68t$ gives us:

$$\left(68 \sqrt{t}\right)^2 = \left(68t\right)^2$$

Expanding the Squared Terms

Now, let's expand the squared terms on both sides of the equation:

$$\left(68 \sqrt{t}\right)^2 = 68^2 \left(\sqrt{t}\right)^2$$

$$\left(68t\right)^2 = 68^2 t^2$$

Simplifying the Equation

Simplifying the equation further, we get:

$$68^2 \left(\sqrt{t}\right)^2 = 68^2 t^2$$

Since $\left(\sqrt{t}\right)^2 = t$, we can simplify the equation to:

$$68^2 t = 68^2 t^2$$

Dividing Both Sides

To isolate $t$, we can divide both sides of the equation by $68^2$. This will help us get rid of the $68^2$ term and make it easier to solve for $t$. Dividing both sides of the equation by $68^2$ gives us:

$$\frac{68^2 t}{68^2} = \frac{68^2 t^2}{68^2}$$

Simplifying the Fraction

Simplifying the fraction, we get:

$$t = t^2$$

Moving Terms to One Side

To isolate $t$, we can move all the terms to one side of the equation. Subtracting $t^2$ from both sides of the equation gives us:

$$t - t^2 = 0$$

Factoring the Equation

The equation $t - t^2 = 0$ can be factored as:

$$t(1 - t) = 0$$

Solving for t

To solve for $t$, we can set each factor equal to zero and solve for $t$. Setting the first factor equal to zero gives us:

$$t = 0$$

Setting the second factor equal to zero gives us:

$$1 - t = 0$$

Solving for $t$, we get:

$$t = 1$$

In this article, we solved for time, denoted by the variable $t$, in the equation $68 \sqrt{t} = 68t$. We used a step-by-step approach to isolate $t$ and find its value. The equation involved a square root, which we eliminated by squaring both sides of the equation. We then simplified the equation and divided both sides by $68^2$ to isolate $t$. Finally, we factored the equation and solved for $t$ to find its value.

The final answer is $\boxed{0, 1}$.
Solving for Time: A Q&A Guide to Understanding the Equation $68 \sqrt{t} = 68t$

In our previous article, we solved for time, denoted by the variable $t$, in the equation $68 \sqrt{t} = 68t$. We used a step-by-step approach to isolate $t$ and find its value. However, we understand that some readers may still have questions about the equation and the solution. In this article, we will address some of the most frequently asked questions about the equation and provide additional insights to help readers better understand the solution.

Q: What is the equation $68 \sqrt{t} = 68t$ trying to solve?

A: The equation $68 \sqrt{t} = 68t$ is trying to solve for the value of $t$ that satisfies the equation. In other words, we are trying to find the value of $t$ that makes the equation true.

Q: Why do we need to square both sides of the equation?

A: We need to square both sides of the equation to eliminate the square root. By squaring both sides, we can get rid of the square root and make it easier to solve for $t$.

Q: What happens if we don't square both sides of the equation?

A: If we don't square both sides of the equation, we will be left with an equation that involves a square root. This can make it difficult to solve for $t$, as we will have to deal with the square root.

Q: Why do we need to divide both sides of the equation by $68^2$?

A: We need to divide both sides of the equation by $68^2$ to isolate $t$. By dividing both sides by $68^2$, we can get rid of the $68^2$ term and make it easier to solve for $t$.

Q: What is the significance of the final answer $\boxed{0, 1}$?

A: The final answer $\boxed{0, 1}$ represents the two possible values of $t$ that satisfy the equation. In other words, $t$ can be either 0 or 1, and both values make the equation true.

Q: Can we use this method to solve other equations involving square roots?

A: Yes, we can use this method to solve other equations involving square roots. The key is to square both sides of the equation to eliminate the square root, and then simplify the equation to isolate the variable.

Q: What are some common mistakes to avoid when solving equations involving square roots?

A: Some common mistakes to avoid when solving equations involving square roots include:

• Not squaring both sides of the equation
• Not simplifying the equation after squaring both sides
• Not isolating the variable
• Not checking the solutions to make sure they satisfy the original equation

In this article, we addressed some of the most frequently asked questions about the equation $68 \sqrt{t} = 68t$ and provided additional insights to help readers better understand the solution. We hope that this article has been helpful in clarifying any confusion and providing a deeper understanding of the equation and its solution.

• Always square both sides of the equation to eliminate the square root
• Simplify the equation after squaring both sides
• Isolate the variable to make it easier to solve for
• Check the solutions to make sure they satisfy the original equation

By following these tips, you can become more confident in your ability to solve equations involving square roots and tackle more complex problems with ease.