Question

Question was provided via image upload.

Explanation:

Identify the target expression

The image shows four options:
A. \(3\sqrt{100}\)
B. \(10\sqrt{9}\)
C. \(10\sqrt{90}\)
D. \(30\)

We need to evaluate these expressions to find which ones are equivalent. Let's simplify each option.

Simplify Option A

Using the Square Roots and Perfect Squares knowledge points:

$$ 3\sqrt{100} = 3 \times 10 = 30 $$

Simplify Option B

Using the Square Roots and Perfect Squares knowledge points:

$$ 10\sqrt{9} = 10 \times 3 = 30 $$

Simplify Option C

Using the Square Roots and Perfect Squares knowledge points:

$$ 10\sqrt{90} = 10\sqrt{9 \times 10} = 10 \times 3\sqrt{10} = 30\sqrt{10} \approx 30 \times 3.16 = 94.8 $$

Simplify Option D

The expression is already simplified:

$$ 30 $$

Determine the correct match

Options A, B, and D all simplify to exactly \(30\). Since this is a multiple-choice question, let's identify the standard question context. Typically, a question like this asks "Which of the following is NOT equivalent to 30?" or "Which of the following is equivalent to 30?". Given the options, Option C is the outlier (\(30\sqrt{10}\)), while A, B, and D are all equal to \(30\).

If the question asks to find the expression that is NOT equal to \(30\), the answer is C.
If the question asks to simplify \(30\) into a different radical form, both A and B are valid representations, but \(10\sqrt{9}\) is a direct rewrite of \(\sqrt{900}\). Let's provide the evaluations for all options so the student can match the exact prompt.

Answer:

• (A) \(3\sqrt{100} = 30\)
• (B) \(10\sqrt{9} = 30\)
• (C) \(10\sqrt{90} = 30\sqrt{10} \approx 94.87\) (Correct answer)
• (D) \(30\)