Solve: √9·3² + 2³·√4 | Mixed Operations Expression

Q: Do I solve radicals or exponents first?

Both radicals and exponents have the same priority in PEMDAS! Work from left to right when they appear together. In this problem, $ \sqrt{9} $ and $ 3^2 $ can be solved in either order.

Q: Why can't I just work left to right through everything?

Order of operations (PEMDAS) ensures everyone gets the same answer! Without it, $ 3 \cdot 3^2 $ could be interpreted as $ (3 \cdot 3)^2 = 81 $ instead of the correct $ 3 \cdot 9 = 27 $.

Q: What if I get a different answer when checking?

If your check doesn't work, go back and re-evaluate each step. Make sure you calculated $ \sqrt{9} = 3 $, $ 3^2 = 9 $, $ 2^3 = 8 $, and $ \sqrt{4} = 2 $ correctly.

Q: Can I use a calculator for the square roots?

Absolutely! But try to recognize perfect squares like $ \sqrt{9} = 3 $ and $ \sqrt{4} = 2 $ without a calculator. It makes the problem much faster!

Q: Why do we multiply before adding in PEMDAS?

Multiplication represents repeated addition, so it's a 'stronger' operation. Think of $ 3 \cdot 9 + 16 $ as 'three groups of 9, plus 16 more' rather than mixing everything together.

Order of Operations with Radicals and Exponents

Solve:

$\sqrt{9}\cdot3^2+2^3\cdot\sqrt{4}$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve:

$\sqrt{9}\cdot3^2+2^3\cdot\sqrt{4}$

Step-by-step solution

First, we need to evaluate the square roots: $\sqrt{9} = 3$ and $\sqrt{4} = 2$ .

Substitute these values back into the expression:

$3\cdot3^2+2^3\cdot2$

Calculate each term separately:

$3^2 = 9$ , so $3\cdot9 = 27$
$2^3 = 8$ , so $8\cdot2 = 16$

Add these values together:

$27+16=43$

Final Answer

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Evaluate radicals and exponents before multiplication and addition
Technique: Calculate $\sqrt{9} = 3$ and $3^2 = 9$ first
Check: Substitute values: 3·9 + 8·2 = 27 + 16 = 43 ✓

Common Mistakes

Avoid these frequent errors

Adding before completing multiplication
Don't try to add 27 + 2³ = 35 then multiply by 2 = 70! This ignores order of operations and gives wrong answers. Always complete all multiplications first, then add the final results.

Practice Quiz

Test your knowledge with interactive questions

What is the result of the following equation?

$36-4\div2$

FAQ

Everything you need to know about this question

Do I solve radicals or exponents first?

Both radicals and exponents have the same priority in PEMDAS! Work from left to right when they appear together. In this problem, $\sqrt{9}$ and $3^2$ can be solved in either order.

Why can't I just work left to right through everything?

Order of operations (PEMDAS) ensures everyone gets the same answer! Without it, $3 \cdot 3^2$ could be interpreted as $(3 \cdot 3)^2 = 81$ instead of the correct $3 \cdot 9 = 27$ .

What if I get a different answer when checking?

If your check doesn't work, go back and re-evaluate each step. Make sure you calculated $\sqrt{9} = 3$ , $3^2 = 9$ , $2^3 = 8$ , and $\sqrt{4} = 2$ correctly.

Can I use a calculator for the square roots?

Absolutely! But try to recognize perfect squares like $\sqrt{9} = 3$ and $\sqrt{4} = 2$ without a calculator. It makes the problem much faster!

Why do we multiply before adding in PEMDAS?

Multiplication represents repeated addition, so it's a 'stronger' operation. Think of $3 \cdot 9 + 16$ as 'three groups of 9, plus 16 more' rather than mixing everything together.

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