Solve Square Root Problem: Finding √64

Q: How do I remember which numbers are 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 $, $ 7^2 = 49 $, $ 8^2 = 64 $, $ 9^2 = 81 $, and $ 10^2 = 100 $.

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

For numbers like $ \sqrt{50} $, you'll get a decimal answer or need to simplify using factors. Perfect squares like 64 always give you clean, whole number answers!

Q: How can I check my answer quickly?

Simply square your answer! If you think $ \sqrt{64} = 8 $, check: $ 8 \times 8 = 64 $ ✓. If it matches the original number, you're correct!

Q: What's the difference between 64 and √64?

64 is just the number itself. $ \sqrt{64} $ is asking 'what number times itself equals 64?' The answer is 8, so $ \sqrt{64} = 8 $.

Square Roots with Perfect Squares

$\sqrt{64}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

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

00:11 Let's break down 64 to 8 squared

00:15 Let's use this formula in our exercise

00:20 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

$\sqrt{64}=$

Step-by-step solution

To solve this problem, we'll determine the square root of 64, following these steps:

Step 1: Identify the number whose square root we need to find. The number given is 64.
Step 2: Determine which number, when multiplied by itself, equals 64.
Step 3: Recall that $8 \times 8 = 64$ .

Now, let's work through each step:

Step 1: We are tasked with finding $\sqrt{64}$ . The problem involves identifying the number which, when squared, results in 64.
Step 2: To find this number, we'll check our knowledge of squares. We know that 8 is a significant integer whose square results in 64.
Step 3: Compute: $8 \times 8 = 64$ . Hence, $8$ meets the requirement.

We find that the solution to the problem is $\sqrt{64} = 8$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Square root asks which number times itself equals the given value
Technique: Recognize that $8 \times 8 = 64$ so $\sqrt{64} = 8$
Check: Verify by squaring your answer: $8^2 = 64$ ✓

Common Mistakes

Avoid these frequent errors

Confusing square root with division
Don't divide 64 by 2 to get 32 = wrong answer! Square root is not division - it asks what number multiplied by itself gives 64. Always think: what number times itself equals the given number?

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

How do I remember which numbers are perfect squares?

Practice the multiplication tables! Know that $1^2 = 1$ , $2^2 = 4$ , $3^2 = 9$ , $4^2 = 16$ , $5^2 = 25$ , $6^2 = 36$ , $7^2 = 49$ , $8^2 = 64$ , $9^2 = 81$ , and $10^2 = 100$ .

What if the number isn't a perfect square?

For numbers like $\sqrt{50}$ , you'll get a decimal answer or need to simplify using factors. Perfect squares like 64 always give you clean, whole number answers!

Is there a negative answer too?

Technically, both 8 and -8 when squared give 64. However, the principal square root symbol $\sqrt{}$ always means the positive answer, so $\sqrt{64} = 8$ .

How can I check my answer quickly?

Simply square your answer! If you think $\sqrt{64} = 8$ , check: $8 \times 8 = 64$ ✓. If it matches the original number, you're correct!

What's the difference between 64 and √64?

64 is just the number itself. $\sqrt{64}$ is asking 'what number times itself equals 64?' The answer is 8, so $\sqrt{64} = 8$ .

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