Solve the Square Root Equation: √x = 6

Q: Why do I need to square both sides?

Squaring both sides is the only way to eliminate the square root symbol! When you square $ \sqrt{x} $, you get just x, which is what we need to solve for.

Q: What does squaring both sides mean exactly?

It means raising everything on each side to the power of 2. So $ \sqrt{x} = 6 $ becomes $ (\sqrt{x})^2 = 6^2 $.

Q: How do I know $ (\sqrt{x})^2 = x $ ?

By definition! The square root and squaring are opposite operations. They cancel each other out, just like multiplication and division do.

Q: Could x be negative in this problem?

No! Since we need $ \sqrt{x} = 6 $, and square roots of real numbers are always non-negative, x must be positive. Also, $ \sqrt{\text{negative number}} $ isn't defined in real numbers.

Q: How can I check my answer?

Substitute your answer back into the original equation: $ \sqrt{36} = 6 $. Since this is true, x = 36 is correct!

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 solve this, we'll square both sides of the equation to isolate X.

00:14 Notice that the square and the square root cancel each other out, making our equation simpler.

00:23 Now, let's calculate the exponent to find X.

00:27 And there we have it! This is our solution to the equation. Good job following along!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\sqrt{x}=6$

2

Step-by-step solution

To solve this problem, we will perform the following steps:

Step 1: Square both sides of the equation $\sqrt{x} = 6$ .
Step 2: Simplify the equation to find $x$ .

Let's carry out each step in detail:

Step 1: Square both sides of the equation:
$\ (\sqrt{x})^2 = 6^2$

Step 2: Simplify the equation:
Since $(\sqrt{x})^2 = x$ , we have $x = 36$ .

Therefore, the value of $x$ is 36.

3

Final Answer

36

Key Points to Remember

Essential concepts to master this topic

Rule: Square both sides to eliminate the square root symbol
Technique: $(\sqrt{x})^2 = x$ and $6^2 = 36$
Check: Substitute back: $\sqrt{36} = 6$ ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting instead of squaring both sides
Don't try to isolate x by adding 6 to both sides = $\sqrt{x} + 6 = 12$ ! This doesn't eliminate the square root and makes the problem unsolvable. Always square both sides when you have $\sqrt{x} = \text{number}$ .

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{4}=$

FAQ

Everything you need to know about this question

Why do I need to square both sides?

+

Squaring both sides is the only way to eliminate the square root symbol! When you square $\sqrt{x}$ , you get just x, which is what we need to solve for.

What does squaring both sides mean exactly?

+

It means raising everything on each side to the power of 2. So $\sqrt{x} = 6$ becomes $(\sqrt{x})^2 = 6^2$ .

How do I know $(\sqrt{x})^2 = x$ ?

+

By definition! The square root and squaring are opposite operations. They cancel each other out, just like multiplication and division do.

Could x be negative in this problem?

+

No! Since we need $\sqrt{x} = 6$ , and square roots of real numbers are always non-negative, x must be positive. Also, $\sqrt{\text{negative number}}$ isn't defined in real numbers.

How can I check my answer?

+

Substitute your answer back into the original equation: $\sqrt{36} = 6$ . Since this is true, x = 36 is correct!

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Solve the Square Root Equation: √x = 6

Square Root Equations with Squaring Method

❤️ Continue Your Math Journey!

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 does squaring both sides mean exactly?

How do I know $(\sqrt{x})^2 = x$ ?

Could x be negative in this problem?

How can I check my answer?

🌟 Unlock Your Math Potential

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Solve the Square Root Equation: √x = 6

Square Root Equations with Squaring Method

❤️ Continue Your Math Journey!

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 does squaring both sides mean exactly?

How do I know (x)2=x (\sqrt{x})^2 = x (x​)2=x?

Could x be negative in this problem?

How can I check my answer?

🌟 Unlock Your Math Potential

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