Solve the Square Root Equation: √x = 2

Q: Why do we square both sides instead of just removing the square root?

The square root and squaring are inverse operations that cancel each other out. Just removing the symbol doesn't follow mathematical rules - you must perform the same operation on both sides to keep the equation balanced.

Q: How do I check if my answer is correct?

Substitute your value back into the original equation. For example: if $ x = 4 $, then $ \sqrt{4} = 2 $ ✓. If both sides match, you're correct!

Q: Can square root equations have more than one answer?

Simple square root equations like $ \sqrt{x} = 2 $ have one positive solution. However, if you square an equation that wasn't originally a square root, you might get extra solutions that don't work.

Q: What's the difference between √x = 2 and x² = 4?

Great question! $ \sqrt{x} = 2 $ has one solution: $ x = 4 $. But $ x^2 = 4 $ has two solutions: $ x = 4 $ and $ x = -4 $, because both positive and negative numbers can be squared.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's find the value of X in this equation.

00:07 To isolate X, we'll square both sides of the equation.

00:15 Notice how the square and square root operations cancel each other out, making our work simpler.

00:21 Now, let's break down the power into multiplication and calculate the result step by step.

00:27 And there we have it! We've found our solution for X. Let's check if it makes sense.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\sqrt{x}=2$

2

Step-by-step solution

To solve the problem, follow these steps:

Step 1: Begin with the equation $\sqrt{x} = 2$ .
Step 2: Square both sides of the equation to eliminate the square root.
Step 3: Simplify the resulting equation to find $x$ .

Now, let's proceed through each step:
Step 1: The given equation is $\sqrt{x} = 2$ .
Step 2: Square both sides: $(\sqrt{x})^2 = 2^2$ .
Step 3: This simplifies to $x = 4$ .

Therefore, the value of $x$ that satisfies $\sqrt{x} = 2$ is $x = 4$ .

Matching this solution with the provided choices, the correct answer is choice 3, which is 4.

3

Final Answer

4

Key Points to Remember

Essential concepts to master this topic

Rule: Square both sides to eliminate the square root symbol
Technique: $(\sqrt{x})^2 = 2^2$ becomes $x = 4$
Check: Substitute back: $\sqrt{4} = 2$ confirms the solution ✓

Common Mistakes

Avoid these frequent errors

Forgetting to square both sides completely
Don't just remove the square root symbol without squaring = leaves the equation unsolved! This gives you incomplete work instead of the actual answer. Always square both sides of the equation simultaneously.

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 we square both sides instead of just removing the square root?

+

The square root and squaring are inverse operations that cancel each other out. Just removing the symbol doesn't follow mathematical rules - you must perform the same operation on both sides to keep the equation balanced.

What if I get a negative number under the square root?

+

For real numbers, we can't take the square root of negative values. If you get $x < 0$ , double-check your work - there might be no real solution to the equation.

How do I check if my answer is correct?

+

Substitute your value back into the original equation. For example: if $x = 4$ , then $\sqrt{4} = 2$ ✓. If both sides match, you're correct!

Can square root equations have more than one answer?

+

Simple square root equations like $\sqrt{x} = 2$ have one positive solution. However, if you square an equation that wasn't originally a square root, you might get extra solutions that don't work.

What's the difference between √x = 2 and x² = 4?

+

Great question! $\sqrt{x} = 2$ has one solution: $x = 4$ . But $x^2 = 4$ has two solutions: $x = 4$ and $x = -4$ , because both positive and negative numbers can be squared.

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Solve the Square Root Equation: √x = 2

Square Root Equations with Integer Solutions

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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 we square both sides instead of just removing the square root?

What if I get a negative number under the square root?

How do I check if my answer is correct?

Can square root equations have more than one answer?

What's the difference between √x = 2 and x² = 4?

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