Solve 18² - (100 + √9): Mixed Operations Expression

Q: Why do I evaluate 18² and √9 before doing the subtraction?

Because of PEMDAS (order of operations)! Exponents and square roots come before addition and subtraction. You must calculate $ 18^2 = 324 $ and $ \sqrt{9} = 3 $ first.

Q: How do I remember which operations to do first?

Use PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. For this problem: do $ 18^2 $ and $ \sqrt{9} $ first, then (100 + 3), then subtract!

Q: Is √9 the same as 9²?

No! $ \sqrt{9} = 3 $ (what number times itself gives 9), but $ 9^2 = 81 $ (9 times 9). The square root undoes squaring.

Q: Why is the answer 221 and not one of the other choices?

Following PEMDAS step-by-step: $ 18^2 = 324 $, $ \sqrt{9} = 3 $, so we have 324 - (100 + 3) = 324 - 103 = 221. Any other answer means skipping steps in the order of operations!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem together.

00:08 First, break down the number 9 into three to the power of 2.

00:17 Remember, the square root of a square cancels out the square.

00:22 Now, let's apply this formula to our exercise.

00:31 Make sure to calculate anything inside parentheses first.

00:39 Next, find the square of 18.

00:44 Great job! And that's how we solve the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$18^2-(100+\sqrt{9})=$

2

Step-by-step solution

The given expression is $18^2-(100+\sqrt{9})$

We need to follow the order of operations (PEMDAS/BODMAS), which stands for:

Parentheses
Exponents (i.e., powers and square roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)

Let's solve step by step:

Step 1: Evaluate the exponent and the square root in the expression:

$18^2 = 324$
$\sqrt{9} = 3$

So, the expression becomes $324 - (100 + 3)$

Step 2: Simplify the parentheses:

$100+3=103$

So, the expression becomes $324 - 103$

Step 3: Subtract:

$324-103=221$

Therefore, the value of the expression $18^2-(100+\sqrt{9})$ is 221.

3

Final Answer

221

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Evaluate exponents and square roots before other operations
Technique: Calculate $18^2 = 324$ and $\sqrt{9} = 3$ first
Check: Verify 324 - (100 + 3) = 324 - 103 = 221 ✓

Common Mistakes

Avoid these frequent errors

Not following PEMDAS order correctly
Don't subtract 18² - 100 first = 224! This ignores parentheses and gives the wrong result. Always evaluate exponents and square roots first, then handle parentheses, then subtract from left to right.

Practice Quiz

Test your knowledge with interactive questions

$6+\sqrt{64}-4=$

FAQ

Everything you need to know about this question

Why do I evaluate 18² and √9 before doing the subtraction?

+

Because of PEMDAS (order of operations)! Exponents and square roots come before addition and subtraction. You must calculate $18^2 = 324$ and $\sqrt{9} = 3$ first.

What if I accidentally calculate 18² - 100 first?

+

You'll get the wrong answer! If you do 324 - 100 = 224, then add 3, you get 227 instead of 221. Always handle what's inside parentheses completely before subtracting.

How do I remember which operations to do first?

+

Use PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. For this problem: do $18^2$ and $\sqrt{9}$ first, then (100 + 3), then subtract!

Is √9 the same as 9²?

+

No! $\sqrt{9} = 3$ (what number times itself gives 9), but $9^2 = 81$ (9 times 9). The square root undoes squaring.

Why is the answer 221 and not one of the other choices?

+

Following PEMDAS step-by-step: $18^2 = 324$ , $\sqrt{9} = 3$ , so we have 324 - (100 + 3) = 324 - 103 = 221. Any other answer means skipping steps in the order of operations!

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Solve 18² - (100 + √9): Mixed Operations Expression

Order of Operations with Exponents and Radicals

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