Find the Square Root: Solving √36 Step by Step

Square Root Calculation with Perfect Squares

36= \sqrt{36}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Square root of any number (X) squared, root cancels square
00:15 We'll break down 36 to 6 squared
00:20 We'll use this formula in our exercise
00:23 Root and square cancel each other
00:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

36= \sqrt{36}=

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Understand the definition of a square root.
  • Step 2: Identify which integer, when squared, gives 36.
  • Step 3: Verify this integer meets the required condition.
  • Step 4: Choose the correct answer from the given choices.

Now, let's work through each step:
Step 1: A square root of a number is a value that, when multiplied by itself, gives the original number. Here, we want y y such that y2=36 y^2 = 36 .
Step 2: We test integer values to find which one squared equals 36. Testing y=1,2,3,4,5, y = 1, 2, 3, 4, 5, and 6 6 gives:
- 12=1 1^2 = 1
- 22=4 2^2 = 4
- 32=9 3^2 = 9
- 42=16 4^2 = 16
- 52=25 5^2 = 25
- 62=36 6^2 = 36

Step 3: The integer 6 6 satisfies 62=36 6^2 = 36 . Therefore, 36=6 \sqrt{36} = 6 .

Step 4: The correct choice from the given answer choices is 6 (Choice 4).

Hence, the square root of 36 is 6 \mathbf{6} .

3

Final Answer

6

Key Points to Remember

Essential concepts to master this topic
  • Definition: Square root finds which number multiplied by itself equals the original
  • Method: Test integers systematically: 62=6×6=36 6^2 = 6 \times 6 = 36
  • Verification: Check by squaring your answer: 62=36 6^2 = 36 confirms 36=6 \sqrt{36} = 6

Common Mistakes

Avoid these frequent errors
  • Confusing square root with division by 2
    Don't think 36=36÷2=18 \sqrt{36} = 36 \div 2 = 18 ! This gives a completely wrong answer because division and square root are different operations. Always find which number times itself equals 36.

Practice Quiz

Test your knowledge with interactive questions

\( \sqrt{36}= \)

FAQ

Everything you need to know about this question

How do I know when I've found the right square root?

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When you multiply your answer by itself and get the original number! For example, since 6×6=36 6 \times 6 = 36 , we know 36=6 \sqrt{36} = 6 .

Do I need to memorize all the perfect squares?

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It helps! Start with these common ones: 12=1 1^2 = 1 , 22=4 2^2 = 4 , 32=9 3^2 = 9 , 42=16 4^2 = 16 , 52=25 5^2 = 25 , 62=36 6^2 = 36 . Practice makes them automatic!

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

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Then the answer won't be a whole number. For example, 35 \sqrt{35} is between 5 and 6, but it's not exactly either one. You'd need a calculator for the exact decimal.

Why do we only consider positive square roots?

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The radical symbol \sqrt{} means the principal (positive) square root by definition. While both 6 and -6 when squared equal 36, 36 \sqrt{36} specifically means the positive answer: 6.

Is there a pattern to help me find square roots faster?

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Yes! Look at the last digit of the number. For example, numbers ending in 6 (like 36) have square roots ending in 4 or 6. This can help you guess and check more efficiently.

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