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

Which of the following is equivalent to the expression below?

$$ $$ 10,000^1 $$

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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