Solve: 81 + Square Root of 81 + 10 Expression

Q: Why do I calculate the square root before adding?

The order of operations (PEMDAS) says to handle exponents (including square roots) before addition. Square roots are considered exponent operations, so $ \sqrt{81} $ must be calculated first!

Q: How do I know that √81 equals 9?

Ask yourself: "What number times itself equals 81?" Since $ 9 \times 9 = 81 $, we know $ \sqrt{81} = 9 $. Perfect squares like 81 have nice whole number square roots!

Q: What if I can't remember the square root of 81?

Try thinking of multiplication tables: $ 9 \times 9 = 81 $. You can also list perfect squares: $ 1^2=1, 2^2=4, 3^2=9, ...9^2=81 $.

Q: Do I add from left to right after finding the square root?

Yes! After calculating $ \sqrt{81} = 9 $, you have $ 81 + 9 + 10 $. Add from left to right: $ 81 + 9 = 90 $, then $ 90 + 10 = 100 $.

Order of Operations with Square Roots

$81+\sqrt{81}+10=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this math problem together.

00:08 First, find the square root of eighty-one.

00:12 Now, follow the order of operations from left to right.

00:16 We'll do one calculation at a time, then move on.

00:20 And that's how we solve the problem. Well done!

Step-by-step written solution

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Understand the problem

$81+\sqrt{81}+10=$

Step-by-step solution

To solve the expression $81+\sqrt{81}+10$ , we need to follow the order of operations, often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Here, the expression contains a square root, which is a type of exponent operation. Therefore, we will handle the square root first:

Find the square root of 81, which is calculated as follows: $\sqrt{81} = 9$ .

Now substitute the result back into the original expression:

$81 + 9 + 10$

Next, perform the addition operations from left to right:

First, add 81 and 9: $81 + 9 = 90$ .
Then, add the result to 10: $90 + 10 = 100$ .

Therefore, the final result of the expression $81+\sqrt{81}+10$ is:

$100$

Final Answer

$100$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Handle square roots first as exponent operations
Technique: Calculate $\sqrt{81} = 9$ , then add left to right
Check: Verify $81 + 9 + 10 = 100$ by working step-by-step ✓

Common Mistakes

Avoid these frequent errors

Adding numbers before calculating the square root
Don't add 81 + 81 + 10 = 172 first! This ignores the square root symbol and gives the wrong answer. Always calculate $\sqrt{81} = 9$ first following PEMDAS order of operations.

Practice Quiz

Test your knowledge with interactive questions

$\sqrt{4}=$

FAQ

Everything you need to know about this question

Why do I calculate the square root before adding?

The order of operations (PEMDAS) says to handle exponents (including square roots) before addition. Square roots are considered exponent operations, so $\sqrt{81}$ must be calculated first!

How do I know that √81 equals 9?

Ask yourself: "What number times itself equals 81?" Since $9 \times 9 = 81$ , we know $\sqrt{81} = 9$ . Perfect squares like 81 have nice whole number square roots!

What if I can't remember the square root of 81?

Try thinking of multiplication tables: $9 \times 9 = 81$ . You can also list perfect squares: $1^2=1, 2^2=4, 3^2=9, ...9^2=81$ .

Do I add from left to right after finding the square root?

Yes! After calculating $\sqrt{81} = 9$ , you have $81 + 9 + 10$ . Add from left to right: $81 + 9 = 90$ , then $90 + 10 = 100$ .

Could the answer be one of the other choices like 28?

No way! If you follow PEMDAS correctly, you'll always get 100. Wrong answers like 28 come from ignoring the square root or making calculation errors. Always double-check your work!

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Solve: 81 + Square Root of 81 + 10 Expression

Order of Operations with Square Roots

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I calculate the square root before adding?

How do I know that √81 equals 9?

What if I can't remember the square root of 81?

Do I add from left to right after finding the square root?

Could the answer be one of the other choices like 28?

🌟 Unlock Your Math Potential

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