Solve (Square Root of 25 minus 2²)³ plus 2³: Complete Calculation

Q: Why do I solve what's in parentheses first?

The PEMDAS rule requires parentheses to be solved first! Think of parentheses as a protective barrier - you must completely finish what's inside before moving to operations outside.

Q: Do I calculate the square root or the exponent first inside parentheses?

Both $ \sqrt{25} $ and $ 2^2 $ are equal priority operations. Calculate them in any order, then subtract: $ 5 - 4 = 1 $.

Q: What if I forget to cube the result from parentheses?

You'd get $ 1 + 8 = 9 $ instead of the correct $ 1^3 + 2^3 = 9 $. Lucky coincidence here, but always apply exponents to your parentheses result!

Q: How do I remember the order of operations?

Use PEMDAS: Please Excuse My Dear Aunt Sally. It stands for Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Q: Can I use a calculator for this problem?

Yes! But enter it correctly: (√25-2^2)^3+2^3. Make sure your calculator follows order of operations, or calculate step-by-step as shown.

Order of Operations with Exponents and Roots

Calculate and indicate the answer:

$(\sqrt{25}-2^2)^3+2^3$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 Calculate the root

00:06 Calculate the powers in order to solve the parentheses

00:09 A power is actually the number multiplied by itself according to the exponent

00:13 Let's calculate the powers and then substitute them into our exercise

00:22 Always solve the parentheses first

00:25 1 raised to any power is always equal to 1

00:32 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate and indicate the answer:

$(\sqrt{25}-2^2)^3+2^3$

Step-by-step solution

Previously mentioned in the order of operations that exponents come before multiplication and division which come before addition and subtraction (and parentheses always come before everything),

Let's calculate first the value of the expression inside the parentheses (by calculating the values of the terms with exponents and roots inside the parentheses first) : $(\sqrt{25}-2^2)^3+2^3= (5-4)^3+2^3=1^3+2^3$ where in the second stage we simplified the expression in parentheses,

Next we'll calculate the values of the terms with exponents and perform the addition operation:

$1^3+2^3=1+8=9$ Therefore the correct answer is answer A.

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then exponents, then multiplication/division, then addition/subtraction
Inside Parentheses: Calculate $\sqrt{25} = 5$ and $2^2 = 4$ before subtracting
Final Check: Verify $1^3 + 2^3 = 1 + 8 = 9$ ✓

Common Mistakes

Avoid these frequent errors

Calculating exponents before parentheses operations
Don't calculate $2^3 = 8$ before simplifying $(\sqrt{25}-2^2)$ = wrong order and wrong answer! The parentheses contain operations that must be completed first. Always solve everything inside parentheses completely before moving to exponents outside them.

Practice Quiz

Test your knowledge with interactive questions

$$ 100+5-100+5 $$

FAQ

Everything you need to know about this question

Why do I solve what's in parentheses first?

The PEMDAS rule requires parentheses to be solved first! Think of parentheses as a protective barrier - you must completely finish what's inside before moving to operations outside.

Do I calculate the square root or the exponent first inside parentheses?

Both $\sqrt{25}$ and $2^2$ are equal priority operations. Calculate them in any order, then subtract: $5 - 4 = 1$ .

What if I forget to cube the result from parentheses?

You'd get $1 + 8 = 9$ instead of the correct $1^3 + 2^3 = 9$ . Lucky coincidence here, but always apply exponents to your parentheses result!

How do I remember the order of operations?

Use PEMDAS: Please Excuse My Dear Aunt Sally. It stands for Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Can I use a calculator for this problem?

Yes! But enter it correctly: (√25-2^2)^3+2^3. Make sure your calculator follows order of operations, or calculate step-by-step as shown.

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Solve (Square Root of 25 minus 2²)³ plus 2³: Complete Calculation

Order of Operations with Exponents and 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 solve what's in parentheses first?

Do I calculate the square root or the exponent first inside parentheses?

What if I forget to cube the result from parentheses?

How do I remember the order of operations?

Can I use a calculator for this problem?

🌟 Unlock Your Math Potential

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