Find the Square Root: Solving √256 Step by Step

Q: What if I don't know the square root by memory?

Start by estimating! Since $ 10^2 = 100 $ and $ 20^2 = 400 $, the answer must be between 10 and 20. Test numbers systematically: 15² = 225, 16² = 256 ✓

Q: Are there any tricks to find square roots faster?

Yes! Learn common perfect squares by heart: $ 1^2, 2^2, 3^2... 20^2 $. Also, if a number ends in specific digits, its square root might too. For example, numbers ending in 6 often have square roots ending in 4 or 6.

Q: What's the difference between √256 and -√256?

The symbol $ \sqrt{256} $ specifically means the positive square root, which is 16. While both 16 and -16 when squared equal 256, we conventionally take the positive value unless specified otherwise.

Q: Can I use a calculator for square roots?

Understanding the concept first is crucial! While calculators can verify your answer, practice finding perfect square roots mentally. This builds number sense and helps you recognize patterns in mathematics.

Perfect Squares with Integer Square Roots

$\sqrt{256}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 The square root of any number (X) squared, root cancels square

00:20 We'll break down 256 to 16 squared

00:25 We'll use this formula in our exercise

00:35 Let's calculate the roots

00:40 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

$\sqrt{256}=$

Step-by-step solution

To solve the problem of finding $\sqrt{256}$ , we will determine a number that, when squared, results in 256.

The operation we are performing is finding the square root, which is defined as follows: if $x^2 = n$ , then $x$ is the square root of $n$ .

First, consider the list of perfect squares: 1 (because $1^2 = 1$ ), 4 (because $2^2 = 4$ ), 9 (because $3^2 = 9$ ), 16 (because $4^2 = 16$ ), all the way up to 256 which needs to be checked.

Let's test the number 16:
$16^2 = 16 \times 16 = 256$

This confirms that 16 is the square root of 256.

Therefore, the solution to the problem is $\sqrt{256} = 16$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Square root finds what number multiplied by itself equals the given number
Method: Test if $16^2 = 16 \times 16 = 256$
Verify: Check that your answer squared equals the original number: $16^2 = 256$ ✓

Common Mistakes

Avoid these frequent errors

Confusing square root with division by 2
Don't divide 256 by 2 to get 128 = wrong answer! This confuses square root with halving a number. Always find the number that when multiplied by itself gives the original value.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

How do I know if 256 is a perfect square?

A perfect square is a number that results from multiplying an integer by itself. Try testing numbers like 15, 16, 17 by squaring them. When you find $16^2 = 256$ , you know 256 is a perfect square!

What if I don't know the square root by memory?

Start by estimating! Since $10^2 = 100$ and $20^2 = 400$ , the answer must be between 10 and 20. Test numbers systematically: 15² = 225, 16² = 256 ✓

Are there any tricks to find square roots faster?

Yes! Learn common perfect squares by heart: $1^2, 2^2, 3^2... 20^2$ . Also, if a number ends in specific digits, its square root might too. For example, numbers ending in 6 often have square roots ending in 4 or 6.

What's the difference between √256 and -√256?

The symbol $\sqrt{256}$ specifically means the positive square root, which is 16. While both 16 and -16 when squared equal 256, we conventionally take the positive value unless specified otherwise.

Can I use a calculator for square roots?

Understanding the concept first is crucial! While calculators can verify your answer, practice finding perfect square roots mentally. This builds number sense and helps you recognize patterns in mathematics.

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