Solve the Square Root: Finding √36 Step by Step

Q: Why is the square root of 36 equal to 6?

Because 6 × 6 = 36! The square root asks: what number times itself equals 36? Since 6 multiplied by 6 gives us 36, the answer is 6.

Q: Are there negative square roots too?

Technically yes, since $ (-6) \times (-6) = 36 $ too! But the principal square root (with the √ symbol) always means the positive answer: 6.

Q: How do I remember perfect squares?

Practice the multiplication tables! Know that $ 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36 $, etc. These patterns make square roots much easier.

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

Some numbers like √37 don't have whole number square roots. These are irrational numbers that you'd estimate or use a calculator to find.

Q: Can I use a calculator for square roots?

Yes, but for perfect squares like 36, try to memorize them! It's faster and helps you recognize patterns in more complex problems.

Square Roots with Perfect Squares

$\sqrt{36}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's solve this together.

00:06 First, think of 36 as six, to the power of two.

00:11 The square root of any number like X, squared, just cancels out the square.

00:18 And there you have it! That's the answer.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\sqrt{36}=$

Step-by-step solution

Let's solve the problem step by step:

Step 1: Understand what the square root means.

The square root of a number $n$ is a value that, when multiplied by itself, equals $n$ . This is written as $x = \sqrt{n}$ .

Step 2: Apply this definition to the number $36$ .

We are looking for a number $x$ such that $x^2 = 36$ . This translates to finding $x = \sqrt{36}$ .

Step 3: Determine the correct number.

We know that $6 \times 6 = 36$ . Therefore, the principal square root of $36$ is $6$ .

Thus, the solution to the problem is $\sqrt{36} = 6$ .

Among the given choices, the correct one is: Choice 1: $6$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Square root finds number that multiplies by itself
Method: Think $6 \times 6 = 36$ , so $\sqrt{36} = 6$
Check: Multiply answer by itself: $6^2 = 36$ matches original ✓

Common Mistakes

Avoid these frequent errors

Confusing square root with division
Don't think √36 = 36 ÷ 2 = 18! This uses division instead of finding what number times itself equals 36. Always ask: what number multiplied by itself gives me 36?

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

Why is the square root of 36 equal to 6?

Because 6 × 6 = 36! The square root asks: what number times itself equals 36? Since 6 multiplied by 6 gives us 36, the answer is 6.

Are there negative square roots too?

Technically yes, since $(-6) \times (-6) = 36$ too! But the principal square root (with the √ symbol) always means the positive answer: 6.

How do I remember perfect squares?

Practice the multiplication tables! Know that $1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36$ , etc. These patterns make square roots much easier.

What if the number isn't a perfect square?

Some numbers like √37 don't have whole number square roots. These are irrational numbers that you'd estimate or use a calculator to find.

Can I use a calculator for square roots?

Yes, but for perfect squares like 36, try to memorize them! It's faster and helps you recognize patterns in more complex problems.

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