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

$5+\sqrt{36}-1=$

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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