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

Which of the following is equivalent to the expression below?

$$ $$ 10,000^1 $$

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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