Solve the Square Root Equation: sqrt(x) = 20

Q: What happens if I get a negative number under the square root?

In this problem, we're solving for what's under the square root, so negative results are fine! The equation $ \sqrt{x} = 20 $ tells us x must be positive since square roots of negative numbers aren't real.

Q: How do I know 400 is a perfect square?

Because $ 20 \times 20 = 400 $! When you see $ \sqrt{x} = 20 $, you're looking for the number that gives 20 when you take its square root.

Q: Do I always get whole number answers for square root equations?

Not always! This problem gives a nice whole number (400) because 20 is a whole number. If the right side were something like 2.5, then $ x = 6.25 $ would be the answer.

Q: Can I use a calculator to check my answer?

Absolutely! Type $ \sqrt{400} $ into your calculator. If you get 20, then your answer is correct. This is always a good way to verify your work!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:02 Let's find X together.

00:05 First, we will square both sides to isolate X.

00:12 Remember, squaring and taking the square root cancel each other out.

00:19 Now, break down the exponent into multiplication, and then calculate.

00:25 And that's how we solve the problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\sqrt{x}=20$

2

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Begin with the given equation:

$\sqrt{x} = 20$

Step 2: Square both sides of the equation to eliminate the square root. When you square a square root, you are left with the number inside the square root:

$(\sqrt{x})^2 = 20^2$

Step 3: Simplify both sides of the equation:

$x = 400$

Therefore, the solution to the problem is $x = 400$ .

The correct choice from the provided options is 400.

3

Final Answer

400

Key Points to Remember

Essential concepts to master this topic

Rule: Square both sides to eliminate the square root symbol
Technique: $(\sqrt{x})^2 = 20^2$ becomes $x = 400$
Check: Substitute back: $\sqrt{400} = 20$ ✓

Common Mistakes

Avoid these frequent errors

Only squaring one side of the equation
Don't square just the left side $\sqrt{x}$ = you get x = 20! This ignores the right side and gives the wrong answer. Always square both sides simultaneously to maintain equality.

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

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" a square root - it's a mathematical operation! Squaring both sides is the proper inverse operation that cancels out the square root while keeping the equation balanced.

What happens if I get a negative number under the square root?

+

In this problem, we're solving for what's under the square root, so negative results are fine! The equation $\sqrt{x} = 20$ tells us x must be positive since square roots of negative numbers aren't real.

How do I know 400 is a perfect square?

+

Because $20 \times 20 = 400$ ! When you see $\sqrt{x} = 20$ , you're looking for the number that gives 20 when you take its square root.

Do I always get whole number answers for square root equations?

+

Not always! This problem gives a nice whole number (400) because 20 is a whole number. If the right side were something like 2.5, then $x = 6.25$ would be the answer.

Can I use a calculator to check my answer?

+

Absolutely! Type $\sqrt{400}$ into your calculator. If you get 20, then your answer is correct. This is always a good way to verify your work!

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Solve the Square Root Equation: sqrt(x) = 20

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

What happens if I get a negative number under the square root?

How do I know 400 is a perfect square?

Do I always get whole number answers for square root equations?

Can I use a calculator to check my answer?

🌟 Unlock Your Math Potential

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