Solve the Square Root Equation: Finding X in √x = 2²

Q: Why do I need to square both sides?

Squaring both sides is the inverse operation of taking a square root. When you have $ \sqrt{x} = 4 $, squaring eliminates the square root symbol and gives you $ x = 16 $.

Q: What if I get confused about which operation to do first?

Always follow order of operations! First simplify any powers (like $ 2^2 = 4 $), then work on isolating the variable by squaring both sides.

Q: How do I know if x = 16 is really correct?

Substitute back into the original equation! Check: $ \sqrt{16} = 4 $ and $ 2^2 = 4 $. Since both sides equal 4, your answer is definitely correct!

Q: Can square root equations have negative answers?

For principal square roots (the $ \sqrt{} $ symbol), we only consider positive results. So $ \sqrt{x} $ is always non-negative, making x positive too.

Q: What happens if I don't simplify 2² first?

You'll likely make errors! If you try to work with $ \sqrt{x} = 2^2 $ without simplifying, you might accidentally think x = 4 instead of the correct answer x = 16.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Square both sides to isolate X

00:16 Square and root cancel each other out

00:26 Calculate the exponent

00:31 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\sqrt{x}=2^2$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Simplify the given power.
Step 2: Set up the equation using what we know about square roots.
Step 3: Solve for $x$ using appropriate calculations.

Now, let's work through each step:
Step 1: Simplify $2^2$ . We calculate $2^2 = 4$ .
Step 2: Set up the equation: $\sqrt{x} = 4$ .
Step 3: Square both sides to solve for $x$ .
$x = 4^2 = 16$

Therefore, $\boxed{16}$ is the solution to the problem, which matches with choice 2.

3

Final Answer

16

Key Points to Remember

Essential concepts to master this topic

Rule: Simplify powers first, then isolate the square root
Technique: Square both sides to eliminate square root: $(\sqrt{x})^2 = 4^2$
Check: Substitute back: $\sqrt{16} = 4$ and $2^2 = 4$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the power before solving
Don't solve $\sqrt{x} = 2^2$ by setting x = 4! This skips simplifying $2^2 = 4$ first, leading to the wrong answer x = 4 instead of x = 16. Always simplify powers completely before squaring both sides.

Practice Quiz

Test your knowledge with interactive questions

Which of the following is equivalent to the expression below?

$$ $$ 10,000^1 $$

FAQ

Everything you need to know about this question

Why do I need to square both sides?

+

Squaring both sides is the inverse operation of taking a square root. When you have $\sqrt{x} = 4$ , squaring eliminates the square root symbol and gives you $x = 16$ .

What if I get confused about which operation to do first?

+

Always follow order of operations! First simplify any powers (like $2^2 = 4$ ), then work on isolating the variable by squaring both sides.

How do I know if x = 16 is really correct?

+

Substitute back into the original equation! Check: $\sqrt{16} = 4$ and $2^2 = 4$ . Since both sides equal 4, your answer is definitely correct!

Can square root equations have negative answers?

+

For principal square roots (the $\sqrt{}$ symbol), we only consider positive results. So $\sqrt{x}$ is always non-negative, making x positive too.

What happens if I don't simplify 2² first?

+

You'll likely make errors! If you try to work with $\sqrt{x} = 2^2$ without simplifying, you might accidentally think x = 4 instead of the correct answer x = 16.

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Solve the Square Root Equation: Finding X in √x = 2²

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Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I need to square both sides?

What if I get confused about which operation to do first?

How do I know if x = 16 is really correct?

Can square root equations have negative answers?

What happens if I don't simplify 2² first?

🌟 Unlock Your Math Potential

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