Solve the Square Root Equation: Finding the Number Under √☐ = 8

Q: Why do I need to square both sides?

Squaring is the inverse operation of taking a square root! Just like you subtract to undo addition, you square to undo a square root. This isolates the variable under the radical.

Q: What if the number under the square root isn't a perfect square?

You can still use the same method! For example, if $ \sqrt{x} = 5 $, then $ x = 25 $. The answer will always be the square of the number on the right side.

Q: How do I know if 64 is correct?

Substitute back into the original equation: $ \sqrt{64} = ? $. Since $ 8 \times 8 = 64 $, we know $ \sqrt{64} = 8 $ ✓

Q: Can the answer ever be negative?

In basic square root problems like this, no. Since $ \sqrt{64} = 8 $ (positive), the number under the radical must be positive. We always use the principal (positive) square root.

Q: What's the fastest way to check my work?

Ask yourself: "What number times itself gives me my answer?" For 64, think: $ 8 \times 8 = 64 $, so $ \sqrt{64} = 8 $ ✓

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:06 Square to isolate X

00:19 Square and root cancel each other

00:24 Calculate the exponent

00:27 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\sqrt{☐}=8$

2

Step-by-step solution

To solve the problem $\sqrt{☐} = 8$ , we follow these steps:

Step 1: Identify the equation given, which is $\sqrt{☐} = 8$ .
Step 2: To solve for $☐$ , we need to eliminate the square root. We do this by squaring both sides of the equation:

$(\sqrt{☐})^2 = 8^2$
Step 3: Simplify both sides:

On the left, $(\sqrt{☐})^2$ simplifies to $☐$ , and on the right, $8^2 = 64$ .
Step 4: This gives us the equation $☐ = 64$ .

Thus, the value of $☐$ is 64.

Therefore, the solution to the problem is $64$ .

3

Final Answer

64

Key Points to Remember

Essential concepts to master this topic

Inverse Operations: Square both sides to eliminate square root
Technique: $(\sqrt{x})^2 = x$ and $8^2 = 64$
Check: Substitute back: $\sqrt{64} = 8$ confirms answer ✓

Common Mistakes

Avoid these frequent errors

Squaring only one side of the equation
Don't square just the left side $(\sqrt{☐})^2 = 8$ = wrong answer! This breaks the equality and gives you ☐ = 8 instead of 64. Always square both sides of the equation to maintain balance.

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?

+

Squaring is the inverse operation of taking a square root! Just like you subtract to undo addition, you square to undo a square root. This isolates the variable under the radical.

What if the number under the square root isn't a perfect square?

+

You can still use the same method! For example, if $\sqrt{x} = 5$ , then $x = 25$ . The answer will always be the square of the number on the right side.

How do I know if 64 is correct?

+

Substitute back into the original equation: $\sqrt{64} = ?$ . Since $8 \times 8 = 64$ , we know $\sqrt{64} = 8$ ✓

Can the answer ever be negative?

+

In basic square root problems like this, no. Since $\sqrt{64} = 8$ (positive), the number under the radical must be positive. We always use the principal (positive) square root.

What's the fastest way to check my work?

+

Ask yourself: "What number times itself gives me my answer?" For 64, think: $8 \times 8 = 64$ , so $\sqrt{64} = 8$ ✓

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Solve the Square Root Equation: Finding the Number Under √☐ = 8

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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 the number under the square root isn't a perfect square?

How do I know if 64 is correct?

Can the answer ever be negative?

What's the fastest way to check my work?

🌟 Unlock Your Math Potential

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