Question

select the correct answer.

which expression simplifies to (15x^8)?

( ) (5sqrt{3x^{16}})
( ) (sqrt{75x^{16}})
( ) (sqrt{30x^{16}})
( ) (3sqrt{25x^{16}})

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Analyze the target expression

We want to find which given radical expression simplifies to:

$$ 15x^8 $$

Step 2: Simplify Option 1

Evaluate \( 5\sqrt{3x^{16}} \):

$$ 5\sqrt{3x^{16}} = 5 \cdot \sqrt{3} \cdot \sqrt{x^{16}} = 5\sqrt{3}x^8 $$

This does not equal \( 15x^8 \).

Step 3: Simplify Option 2

Evaluate \( \sqrt{75x^{16}} \):

$$ \sqrt{75x^{16}} = \sqrt{25 \cdot 3 \cdot x^{16}} = 5\sqrt{3}x^8 $$

This does not equal \( 15x^8 \).

Step 4: Simplify Option 3

Evaluate \( \sqrt{30x^{16}} \):

$$ \sqrt{30x^{16}} = \sqrt{30}x^8 $$

This does not equal \( 15x^8 \).

Step 5: Simplify Option 4

Evaluate \( 3\sqrt{25x^{16}} \):

$$ 3\sqrt{25x^{16}} = 3 \cdot \sqrt{25} \cdot \sqrt{x^{16}} = 3 \cdot 5 \cdot x^8 = 15x^8 $$

This matches the target expression.

Answer:

The correct option is:

$$ 3\sqrt{25x^{16}} $$