Solve the Square Root: Finding the Value of √81

Q: Why isn't the square root of 81 equal to 40.5?

Square root is not division! $ \sqrt{81} \neq 81 \div 2 $. Instead, think: what number multiplied by itself gives 81? Since $ 9 \times 9 = 81 $, the answer is 9.

Q: How can I remember perfect squares like 81?

Practice the multiplication table 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, 9^2=81, 10^2=100 $. The more you use them, the faster you'll recognize them!

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

Great question! Numbers like $ \sqrt{80} $ don't have whole number answers. You'd need a calculator or learn about simplifying radicals for those cases.

Q: Can square roots be negative?

When we write $ \sqrt{81} $, we mean the positive square root, which is 9. While both 9 and -9 multiply to give 81, the square root symbol always gives the positive answer.

Q: How do I check my square root answer?

Always multiply your answer by itself! If you think $ \sqrt{81} = 9 $, check: $ 9 \times 9 = 81 $ ✓. If it matches the original number, you're right!

Square Roots with Perfect Square Numbers

$\sqrt{81}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's solve this problem together!

00:06 The square root of a number X squared cancels out the square. It's like a math magic trick!

00:17 Now, let's look at 81. We can break it down into 9 times 9, or 9 squared.

00:24 We'll apply this trick in our exercise to make solving easier.

00:28 And there you have it, the solution to our question. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\sqrt{81}=$

Step-by-step solution

To solve this problem, follow these steps:

Step 1: Understand that the square root of a number $n$ is a value that, when multiplied by itself, equals $n$ .
Step 2: Identify the number whose square is 81. Since $9 \times 9 = 81$ , the square root of 81 is 9.

Therefore, the square root of 81 is $9$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: Square root finds which number multiplied by itself gives the original
Method: Think backwards - what times what equals 81? Since $9 \times 9 = 81$
Check: Multiply your answer by itself: $9 \times 9 = 81$ ✓

Common Mistakes

Avoid these frequent errors

Confusing square root with division by 2
Don't divide 81 by 2 to get 40.5 = wrong answer! Square root is NOT division. Always ask 'what number times itself equals 81?' which is 9.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{100}=$

FAQ

Everything you need to know about this question

Why isn't the square root of 81 equal to 40.5?

Square root is not division! $\sqrt{81} \neq 81 \div 2$ . Instead, think: what number multiplied by itself gives 81? Since $9 \times 9 = 81$ , the answer is 9.

How can I remember perfect squares like 81?

Practice the multiplication table squares: $1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36, 7^2=49, 8^2=64, 9^2=81, 10^2=100$ . The more you use them, the faster you'll recognize them!

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

Great question! Numbers like $\sqrt{80}$ don't have whole number answers. You'd need a calculator or learn about simplifying radicals for those cases.

Can square roots be negative?

When we write $\sqrt{81}$ , we mean the positive square root, which is 9. While both 9 and -9 multiply to give 81, the square root symbol always gives the positive answer.

How do I check my square root answer?

Always multiply your answer by itself! If you think $\sqrt{81} = 9$ , check: $9 \times 9 = 81$ ✓. If it matches the original number, you're right!

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