Solve 2×(3³ + √144): Order of Operations Practice

Q: Why can't I just multiply 2 by each term in the parentheses first?

Because of PEMDAS! Parentheses must be solved completely before any outside multiplication. You need $ 3^3 + \sqrt{144} = 39 $ first, then multiply by 2.

Q: How do I calculate 3³ quickly?

$ 3^3 $ means three multiplied by itself three times: $ 3 \times 3 \times 3 = 9 \times 3 = 27 $. Break it into steps!

Q: What if I don't remember that √144 = 12?

Think of perfect squares! Since $ 12 \times 12 = 144 $, we know $ \sqrt{144} = 12 $. Practice common perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.

Q: Can I solve the exponent and square root in any order?

Yes! Both exponents and radicals have the same priority in PEMDAS. You can calculate $ 3^3 $ first or $ \sqrt{144} $ first - just make sure to do both before adding.

Q: What happens if I add before solving the exponent and root?

You'll get completely wrong numbers! For example: $ 3 + 144 = 147 $, then trying operations on 147 gives nowhere near our answer of 78. Always follow PEMDAS order!

Order of Operations with Exponents and Radicals

$2\times(3^3+\sqrt{144})=$

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Understand the problem

$2\times(3^3+\sqrt{144})=$

Step-by-step solution

To solve the expression $2\times(3^3+\sqrt{144})$ , we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Step 1: Begin by solving the part inside the parentheses $(3^3+\sqrt{144})$ .

Exponents: Calculate $3^3$ .
$3^3$ means $3 \times 3 \times 3 = 27$ .
Roots: Calculate $\sqrt{144}$ .
$\sqrt{144} = 12$ , since 12 is the number that when multiplied by itself gives 144.

Add the results of the exponent and the root: $27 + 12 = 39$ .
Step 2: Multiply the sum by 2:
$2 \times 39 = 78$ .

Therefore, the final answer is $78$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then exponents and roots before multiplication
Technique: Calculate $3^3 = 27$ and $\sqrt{144} = 12$ before adding
Check: Substitute back: $2 \times (27 + 12) = 2 \times 39 = 78$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying 2 by each term inside parentheses first
Don't distribute 2 × (3³ + √144) = 2×3³ + 2×√144 = wrong answer! This ignores PEMDAS order and gives 78 instead of the correct process. Always solve what's inside parentheses completely before multiplying by outside terms.

Practice Quiz

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What is the result of the following equation?

$36-4\div2$

FAQ

Everything you need to know about this question

Why can't I just multiply 2 by each term in the parentheses first?

Because of PEMDAS! Parentheses must be solved completely before any outside multiplication. You need $3^3 + \sqrt{144} = 39$ first, then multiply by 2.

How do I calculate 3³ quickly?

$3^3$ means three multiplied by itself three times: $3 \times 3 \times 3 = 9 \times 3 = 27$ . Break it into steps!

What if I don't remember that √144 = 12?

Think of perfect squares! Since $12 \times 12 = 144$ , we know $\sqrt{144} = 12$ . Practice common perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.

Can I solve the exponent and square root in any order?

Yes! Both exponents and radicals have the same priority in PEMDAS. You can calculate $3^3$ first or $\sqrt{144}$ first - just make sure to do both before adding.

What happens if I add before solving the exponent and root?

You'll get completely wrong numbers! For example: $3 + 144 = 147$ , then trying operations on 147 gives nowhere near our answer of 78. Always follow PEMDAS order!

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