Solve the Square Root Expression: Finding the Value of √4

Q: Why isn't the answer -2 since (-2)² = 4 too?

Great observation! While both $ 2^2 = 4 $ and $ (-2)^2 = 4 $, the square root symbol $ \sqrt{} $ always means the positive answer (called the principal square root).

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

Numbers like $ \sqrt{5} $ or $ \sqrt{8} $ don't have nice whole number answers. You can leave them as square roots or use a calculator for approximate decimal answers.

Square Roots with Perfect Squares

$\sqrt{4}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Root of any number (X) squared, root cancels square

00:10 We'll break down 4 to 2 squared

00:13 We'll use this formula in our exercise

00:16 Root and square cancel each other

00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\sqrt{4}=$

Step-by-step solution

To solve this problem, we'll determine the square root of the number 4.

Step 1: Recognize that the square root of a number is asking for a value that, when multiplied by itself, yields the original number. Here, we seek a number $y$ such that $y^2 = 4$ .
Step 2: Identify that $4$ is a perfect square. The numbers $2$ and $-2$ both satisfy the equation $2^2 = 4$ and $(-2)^2 = 4$ .
Step 3: We usually consider the principal square root, which is the non-negative version. Thus, $\sqrt{4} = 2$ .

Therefore, the solution to the problem is 2, which corresponds to the correct choice from the given options.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Square root asks what number times itself equals the original
Technique: For $\sqrt{4}$ , find what number squared equals 4: $2^2 = 4$
Check: Multiply your answer by itself: $2 \times 2 = 4$ ✓

Common Mistakes

Avoid these frequent errors

Confusing square roots with simple division
Don't think √4 = 4 ÷ 2 = 2 by accident! Square roots aren't division - they ask what number multiplied by itself gives the original. Always ask: what times what equals 4?

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{36}=$

FAQ

Everything you need to know about this question

Why isn't the answer -2 since (-2)² = 4 too?

Great observation! While both $2^2 = 4$ and $(-2)^2 = 4$ , the square root symbol $\sqrt{}$ always means the positive answer (called the principal square root).

How do I know if a number is a perfect square?

A perfect square comes from multiplying a whole number by itself. Common ones to memorize: $1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25$ , etc.

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

Numbers like $\sqrt{5}$ or $\sqrt{8}$ don't have nice whole number answers. You can leave them as square roots or use a calculator for approximate decimal answers.

Is there a pattern to help me remember perfect squares?

Yes! Notice the pattern: $1, 4, 9, 16, 25, 36...$ The differences between consecutive perfect squares follow the odd numbers: 3, 5, 7, 9, 11...

Can I have a square root of a negative number?

In basic algebra, we can't take square roots of negative numbers because no real number times itself gives a negative result. This comes up later in advanced math!

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