Calculate the Square Root: Solving √9 Step by Step

Q: Why is the answer 3 and not -3?

The square root symbol $ \sqrt{} $ always means the principal (positive) square root. While both 3² = 9 and (-3)² = 9, we only consider the positive value unless told otherwise.

Q: What makes 9 a perfect square?

A perfect square is a whole number that equals another whole number multiplied by itself. Since $ 3 \times 3 = 9 $, we say 9 is a perfect square of 3.

Q: How can I remember common perfect squares?

Practice these basics: $ 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25 $. Knowing these by heart makes square root problems much faster!

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

For non-perfect squares like $ \sqrt{8} $, you'll get a decimal approximation or leave it in radical form. Perfect squares like 9 give you exact whole number answers.

Q: Is there a difference between √9 and 9^(1/2)?

No difference! $ \sqrt{9} $ and $ 9^{1/2} $ are just two ways to write the same thing. Both equal 3.

Principal Square Roots with Perfect Squares

$\sqrt{9}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Root of any number (X) squared, root cancels out square

00:11 We'll break down 9 to 3 squared

00:16 We'll use this formula in our exercise

00:19 Root and square cancel each other out

00:22 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

$\sqrt{9}=$

Step-by-step solution

To solve this problem, we want to find the square root of 9.

Step 1: Recognize that a square root is a number which, when multiplied by itself, equals the original number. Thus, we are seeking a number $x$ such that $x^2 = 9$ .

Step 2: Note that 9 is a common perfect square: $9 = 3 \times 3$ . Therefore, the square root of 9 is the number that, when multiplied by itself, gives 9. This number is 3.

Step 3: Since we are interested in the principal square root, we consider only the non-negative value. Hence, the principal square root of 9 is 3.

Therefore, the solution to the problem is $3$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Square root finds number that multiplies by itself
Technique: Recognize 9 = 3 × 3, so √9 = 3
Check: Verify by squaring: 3² = 3 × 3 = 9 ✓

Common Mistakes

Avoid these frequent errors

Including negative answers for principal square root
Don't write √9 = ±3 when asked for just √9 = both +3 and -3! The radical symbol √ means principal (positive) root only. Always give the positive value unless specifically asked for both roots.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

Why is the answer 3 and not -3?

The square root symbol $\sqrt{}$ always means the principal (positive) square root. While both 3² = 9 and (-3)² = 9, we only consider the positive value unless told otherwise.

What makes 9 a perfect square?

A perfect square is a whole number that equals another whole number multiplied by itself. Since $3 \times 3 = 9$ , we say 9 is a perfect square of 3.

How can I remember common perfect squares?

Practice these basics: $1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25$ . Knowing these by heart makes square root problems much faster!

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

For non-perfect squares like $\sqrt{8}$ , you'll get a decimal approximation or leave it in radical form. Perfect squares like 9 give you exact whole number answers.

Is there a difference between √9 and 9^(1/2)?

No difference! $\sqrt{9}$ and $9^{1/2}$ are just two ways to write the same thing. Both equal 3.

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