Solve For $x$.$9 = \sqrt{x}$x = \square$

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Introduction

In mathematics, solving for $x$ in an equation often involves isolating the variable on one side of the equation. When dealing with square root equations, it's essential to understand the properties of square roots and how to manipulate them to find the value of $x$. In this article, we'll explore how to solve for $x$ in the equation $9 = \sqrt{x}$.

Understanding Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because $4 \times 4 = 16$. The square root of a number is denoted by the symbol $\sqrt{}$. In the equation $9 = \sqrt{x}$, we're looking for a value of $x$ such that the square root of $x$ is equal to 9.

Solving for $x$

To solve for $x$, we need to get rid of the square root symbol. We can do this by squaring both sides of the equation. Squaring both sides of the equation $9 = \sqrt{x}$ gives us:

$$9^2 = (\sqrt{x})^2$$

Using the property of exponents that $(a^m)^n = a^{mn}$, we can simplify the right-hand side of the equation:

$$9^2 = x$$

Now, we can evaluate the left-hand side of the equation:

$$81 = x$$

Therefore, the value of $x$ that satisfies the equation $9 = \sqrt{x}$ is $x = 81$.

Checking Our Answer

To verify that our answer is correct, we can plug it back into the original equation:

$$9 = \sqrt{81}$$

Using the property of square roots that $\sqrt{a^2} = a$, we can simplify the right-hand side of the equation:

$$9 = 9$$

Since both sides of the equation are equal, we can conclude that our answer is correct.

Conclusion

Solving for $x$ in a square root equation involves understanding the properties of square roots and manipulating the equation to isolate the variable. By squaring both sides of the equation and simplifying, we can find the value of $x$ that satisfies the equation. In this article, we solved for $x$ in the equation $9 = \sqrt{x}$ and found that $x = 81$.

Additional Examples

Here are a few more examples of solving for $x$ in square root equations:

• $4 = \sqrt{x}$: Squaring both sides of the equation gives us $16 = x$.
• $6 = \sqrt{x}$: Squaring both sides of the equation gives us $36 = x$.
• $8 = \sqrt{x}$: Squaring both sides of the equation gives us $64 = x$.

Tips and Tricks

Here are a few tips and tricks to keep in mind when solving for $x$ in square root equations:

• Make sure to square both sides of the equation to get rid of the square root symbol.
• Simplify the equation by using the properties of exponents and square roots.
• Check your answer by plugging it back into the original equation.

Common Mistakes

Here are a few common mistakes to avoid when solving for $x$ in square root equations:

• Failing to square both sides of the equation.
• Not simplifying the equation properly.
• Not checking the answer by plugging it back into the original equation.

Real-World Applications

Solving for $x$ in square root equations has many real-world applications, including:

• Calculating the area of a square or rectangle.
• Finding the length of a side of a square or rectangle.
• Determining the value of a function at a given point.

Conclusion

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Introduction

In our previous article, we explored how to solve for $x$ in a square root equation. In this article, we'll answer some frequently asked questions about solving for $x$ in square root equations.

Q: What is a square root equation?

A: A square root equation is an equation that contains a square root symbol, $\sqrt{}$. For example, the equation $9 = \sqrt{x}$ is a square root equation.

Q: How do I solve for $x$ in a square root equation?

A: To solve for $x$ in a square root equation, you need to get rid of the square root symbol. You can do this by squaring both sides of the equation. For example, to solve the equation $9 = \sqrt{x}$, you would square both sides of the equation to get $81 = x$.

Q: What if the equation has a variable on both sides?

A: If the equation has a variable on both sides, you need to isolate the variable on one side of the equation. You can do this by adding or subtracting the same value to both sides of the equation. For example, to solve the equation $x + 3 = \sqrt{x}$, you would subtract 3 from both sides of the equation to get $x = \sqrt{x} - 3$.

Q: Can I use a calculator to solve for $x$ in a square root equation?

A: Yes, you can use a calculator to solve for $x$ in a square root equation. However, it's always a good idea to check your answer by plugging it back into the original equation.

Q: What if the equation has a negative number under the square root symbol?

A: If the equation has a negative number under the square root symbol, you need to remember that the square of a negative number is positive. For example, to solve the equation $-\sqrt{x} = 9$, you would square both sides of the equation to get $x = 81$.

Q: Can I use a square root equation to solve a problem in real life?

A: Yes, you can use a square root equation to solve a problem in real life. For example, if you know the area of a square, you can use a square root equation to find the length of a side of the square.

Q: What are some common mistakes to avoid when solving for $x$ in a square root equation?

A: Some common mistakes to avoid when solving for $x$ in a square root equation include:

• Failing to square both sides of the equation.
• Not simplifying the equation properly.
• Not checking the answer by plugging it back into the original equation.

Q: How do I check my answer when solving for $x$ in a square root equation?

A: To check your answer when solving for $x$ in a square root equation, you need to plug your answer back into the original equation. If the equation is true, then your answer is correct.

Conclusion

Solving for $x$ in a square root equation involves understanding the properties of square roots and manipulating the equation to isolate the variable. By squaring both sides of the equation and simplifying, we can find the value of $x$ that satisfies the equation. In this article, we answered some frequently asked questions about solving for $x$ in square root equations.

Additional Resources

Here are some additional resources to help you learn more about solving for $x$ in square root equations:

• Khan Academy: Solving Square Root Equations
• Mathway: Solving Square Root Equations
• Purplemath: Solving Square Root Equations

Conclusion

Solving for $x$ in a square root equation is an essential skill in mathematics. By understanding the properties of square roots and manipulating the equation to isolate the variable, we can find the value of $x$ that satisfies the equation. In this article, we answered some frequently asked questions about solving for $x$ in square root equations.