Solve the Square Root Equation: √x = 1

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

You can't just "remove" the square root symbol! Squaring both sides is the mathematical operation that eliminates the square root while keeping the equation balanced.

Q: What happens when I square the square root?

When you square a square root, they cancel each other out! So $ (\sqrt{x})^2 = x $. The square and square root are inverse operations.

Q: Do I always get a positive answer for square root equations?

Yes! The square root symbol $ \sqrt{x} $ always represents the positive square root, so your answer must make the square root positive or zero.

Square Root Equations with Basic Solving

$\sqrt{x}=1$

$X=?$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 We'll square it to isolate the unknown

00:12 Square and root cancel each other out

00:17 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\sqrt{x}=1$

$X=?$

Step-by-step solution

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

Step 1: Square both sides of the equation.
Step 2: Simplify the resulting expression.

Now, let's work through each step:

Step 1: We have the equation $\sqrt{x} = 1$ .
Square both sides:

$(\sqrt{x})^2 = 1^2$

Step 2: Simplify both sides of the equation.

The left side simplifies to $x$ , since the square and the square root cancel each other out:

$x = 1$

The right side simplifies to 1, so we have:

$x = 1$

Therefore, the solution to the problem is $x = 1$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Square both sides to eliminate the square root symbol
Technique: $(\sqrt{x})^2 = 1^2$ becomes $x = 1$
Check: Substitute back: $\sqrt{1} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to square the right side of the equation
Don't square just the left side $\sqrt{x}$ and leave the right side as 1 = wrong answer x = 1²! This breaks the equality principle. Always square both sides: $(\sqrt{x})^2 = 1^2$ .

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{4}=$

FAQ

Everything you need to know about this question

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

You can't just "remove" the square root symbol! Squaring both sides is the mathematical operation that eliminates the square root while keeping the equation balanced.

What happens when I square the square root?

When you square a square root, they cancel each other out! So $(\sqrt{x})^2 = x$ . The square and square root are inverse operations.

Do I always get a positive answer for square root equations?

Yes! The square root symbol $\sqrt{x}$ always represents the positive square root, so your answer must make the square root positive or zero.

How can I check if my answer is correct?

Substitute your answer back into the original equation. For $x = 1$ : $\sqrt{1} = 1$ ✓. If both sides are equal, you're right!

What if the number under the square root is negative?

In basic math, we can't take the square root of negative numbers! Make sure your solution gives a non-negative value under the square root sign.

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