Calculate the Square Root: Solving √64 Step by Step

Q: What exactly is a square root?

A square root is a number that when multiplied by itself gives you the original number. So $ \sqrt{64} $ asks: "What number times itself equals 64?"

Q: How do I memorize perfect squares?

Start with the basics: $ 1^2 = 1 $, $ 2^2 = 4 $, $ 3^2 = 9 $, $ 4^2 = 16 $, $ 5^2 = 25 $. Practice these daily and gradually work up to $ 12^2 = 144 $!

Q: Can square roots be negative?

When we write $ \sqrt{64} $, we want the positive square root, which is 8. While both 8 and -8 multiply to give 64, the square root symbol always means the positive answer.

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

If it's not a perfect square (like $ \sqrt{50} $), you can estimate between known perfect squares or use a calculator. Since $ 7^2 = 49 $ and $ 8^2 = 64 $, $ \sqrt{50} $ is slightly more than 7.

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 Let's break down 64 into 8 squared

00:06 The square root of any number (X) squared, root cancels square

00:09 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 follow these steps:

Step 1: Recognize what finding a square root means
Step 2: List known perfect squares to identify which one results in 64
Step 3: Verify the square root by calculation

Now, let's work through each step:
Step 1: To find the square root of 64, we seek a number that, when multiplied by itself, equals 64.
Step 2: Consider the sequence of perfect squares: $1^2 = 1$ , $2^2 = 4$ , $3^2 = 9$ , $4^2 = 16$ , $5^2 = 25$ , $6^2 = 36$ , $7^2 = 49$ , $8^2 = 64$ .
Step 3: We see that $8^2 = 64$ . Therefore, the square root of 64 is 8.

Therefore, the solution to this problem is $8$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Find the number that when multiplied by itself equals 64
Method: List perfect squares: $8^2 = 64$
Verify: Check that $8 \times 8 = 64$ ✓

Common Mistakes

Avoid these frequent errors

Confusing square root with squaring the number
Don't calculate 64 × 64 = 4,096! This gives you the square OF 64, not the square root. Always find what number multiplied by itself equals 64.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

What exactly is a square root?

A square root is a number that when multiplied by itself gives you the original number. So $\sqrt{64}$ asks: "What number times itself equals 64?"

How do I memorize perfect squares?

Start with the basics: $1^2 = 1$ , $2^2 = 4$ , $3^2 = 9$ , $4^2 = 16$ , $5^2 = 25$ . Practice these daily and gradually work up to $12^2 = 144$ !

Can square roots be negative?

When we write $\sqrt{64}$ , we want the positive square root, which is 8. While both 8 and -8 multiply to give 64, the square root symbol always means the positive answer.

What if the number isn't a perfect square?

If it's not a perfect square (like $\sqrt{50}$ ), you can estimate between known perfect squares or use a calculator. Since $7^2 = 49$ and $8^2 = 64$ , $\sqrt{50}$ is slightly more than 7.

Why do we need to verify our answer?

Verification catches calculation errors! Simply multiply your answer by itself: $8 \times 8 = 64$ . If it matches the original number under the square root, you're correct!

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