Solve Step-by-Step: (√81 - 3×3) ÷ 4 + 5×5 Expression

Q: Why do I solve the square root before multiplication?

Square roots are considered exponents in PEMDAS! Since $ \sqrt{81} = 81^{1/2} $, you solve it right after parentheses but before multiplication and division.

Q: What if I can't remember what √81 equals?

Think of perfect squares: $ 9 \times 9 = 81 $, so $ \sqrt{81} = 9 $. Practice memorizing perfect squares from 1 to 12 - it makes these problems much faster!

Q: Do I really need to write out every step?

Yes! Writing each step prevents mistakes and helps you track your work. Even if you can do some steps mentally, showing your work helps you catch errors.

Q: Why does the order matter so much?

Mathematical operations have agreed-upon rules so everyone gets the same answer. Without PEMDAS, $ 2 + 3 \times 4 $ could equal 20 or 14 - we need one correct answer!

Q: What happens if I forget the parentheses?

Parentheses group operations together! Without them, $ \sqrt{81} - 3 \times 3 \div 4 + 5 \times 5 $ would be solved completely differently. Always solve what's inside parentheses first.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's solve this problem together!

00:13 First, always take care of anything inside parentheses.

00:17 Next, find the square root of eighty-one. It's nine.

00:21 Place this value back into the problem.

00:25 Remember, multiplication and division come before addition and subtraction.

00:31 Also, the square root of a number squared is just the number itself.

00:48 And, zero divided by any number is always zero.

00:55 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\lbrack(\sqrt{81}-3\times3):4+5\times5\rbrack=$

2

Step-by-step solution

According to the rules of order of arithmetic operations, parentheses are resolved first.

We start by solving the inner parentheses, first we will solve the root using the formula:

$\sqrt{a}=\sqrt{a^2}=a$

$\sqrt{81}=\sqrt{9^2}=9$

The exercise obtained within parentheses is:

$(9-3\times3)$

First we solve the multiplication exercise and then we subtract:

$(9-9)=0$

After solving the inner parentheses, the resulting exercise is:

$0:4+5\times5$

According to the rules of the order of arithmetic operations, we first solve the exercises of multiplication and division, and then subtraction.

We place the two exercises within parentheses to avoid confusion:

$(0:4)+(5\times5)=0+25=25$

3

Final Answer

$25$

Key Points to Remember

Essential concepts to master this topic

Rule: Follow PEMDAS - parentheses, exponents/roots, multiplication/division, addition/subtraction left to right
Technique: Simplify $\sqrt{81} = 9$ first, then solve inside parentheses completely
Check: Substitute final answer: $0 \div 4 + 25 = 25$ ✓

Common Mistakes

Avoid these frequent errors

Solving operations from left to right without considering order
Don't solve $\sqrt{81} - 3 \times 3 \div 4 + 5 \times 5$ left to right = wrong answer! This ignores PEMDAS and gives incorrect results. Always solve parentheses first, then multiplication/division before addition/subtraction.

Practice Quiz

Test your knowledge with interactive questions

$20\div(4+1)-3=$

FAQ

Everything you need to know about this question

Why do I solve the square root before multiplication?

+

Square roots are considered exponents in PEMDAS! Since $\sqrt{81} = 81^{1/2}$ , you solve it right after parentheses but before multiplication and division.

What if I can't remember what √81 equals?

+

Think of perfect squares: $9 \times 9 = 81$ , so $\sqrt{81} = 9$ . Practice memorizing perfect squares from 1 to 12 - it makes these problems much faster!

Do I really need to write out every step?

+

Yes! Writing each step prevents mistakes and helps you track your work. Even if you can do some steps mentally, showing your work helps you catch errors.

Why does the order matter so much?

+

Mathematical operations have agreed-upon rules so everyone gets the same answer. Without PEMDAS, $2 + 3 \times 4$ could equal 20 or 14 - we need one correct answer!

What happens if I forget the parentheses?

+

Parentheses group operations together! Without them, $\sqrt{81} - 3 \times 3 \div 4 + 5 \times 5$ would be solved completely differently. Always solve what's inside parentheses first.

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Solve Step-by-Step: (√81 - 3×3) ÷ 4 + 5×5 Expression

Order of Operations with Square Roots

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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 solve the square root before multiplication?

What if I can't remember what √81 equals?

Do I really need to write out every step?

Why does the order matter so much?

What happens if I forget the parentheses?

🌟 Unlock Your Math Potential

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