Solve the Square Root Equation: Finding X in √x = 7

Q: What does squaring both sides actually do?

Squaring both sides uses the property that $ (\sqrt{x})^2 = x $. So $ \sqrt{x} = 7 $ becomes $ x = 7^2 = 49 $. It's like canceling out the square root!

Q: How can I check if x = 49 is really correct?

Substitute back into the original equation: $ \sqrt{49} = ? $. Since $ \sqrt{49} = 7 $, and our equation was $ \sqrt{x} = 7 $, it works perfectly!

Q: What if the number on the right side was negative?

Great question! If we had $ \sqrt{x} = -7 $, there would be no solution because square roots of real numbers are always positive or zero.

Q: Is this the same as finding what 7 squared equals?

Exactly! When $ \sqrt{x} = 7 $, we're asking "what number has a square root of 7?" The answer is $ 7^2 = 49 $.

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

00:11 Square and root cancel each other out

00:15 Calculate the exponent

00:18 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

$\sqrt{x}=7$

2

Step-by-step solution

To solve this problem, we will eliminate the square root by squaring both sides of the equation.

Step 1: Start with the given equation:
$\sqrt{x} = 7$
Step 2: Square both sides of the equation to eliminate the square root:
$(\sqrt{x})^2 = 7^2$
Step 3: Simplify both sides:
$x = 49$
This calculation shows that when the square root of $x$ is 7, the value of $x$ must be 49 to satisfy the equation.

Therefore, the solution to the problem is $x = 49$ . This matches the correct choice from the given multiple-choice options.

3

Final Answer

49

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 $7^2 = 49$
Check: Substitute back: $\sqrt{49} = 7$ confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Forgetting to square the right side of the equation
Don't just remove the square root and write x = 7! This ignores the fundamental property that squaring eliminates square roots. Always square both sides: $(\sqrt{x})^2 = 7^2$ gives x = 49.

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

Why do I need to square both sides instead of just removing the square root?

+

The square root symbol means "what number times itself equals x?" To find that number, you must undo the square root by squaring. Just removing it breaks the mathematical equality!

What does squaring both sides actually do?

+

Squaring both sides uses the property that $(\sqrt{x})^2 = x$ . So $\sqrt{x} = 7$ becomes $x = 7^2 = 49$ . It's like canceling out the square root!

How can I check if x = 49 is really correct?

+

Substitute back into the original equation: $\sqrt{49} = ?$ . Since $\sqrt{49} = 7$ , and our equation was $\sqrt{x} = 7$ , it works perfectly!

What if the number on the right side was negative?

+

Great question! If we had $\sqrt{x} = -7$ , there would be no solution because square roots of real numbers are always positive or zero.

Is this the same as finding what 7 squared equals?

+

Exactly! When $\sqrt{x} = 7$ , we're asking "what number has a square root of 7?" The answer is $7^2 = 49$ .

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Solve the Square Root Equation: Finding X in √x = 7

Square Root Equations with Basic Squaring

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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 instead of just removing the square root?

What does squaring both sides actually do?

How can I check if x = 49 is really correct?

What if the number on the right side was negative?

Is this the same as finding what 7 squared equals?

🌟 Unlock Your Math Potential

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