Question

Select the correct answer. Which expression is equivalent to \( 8x^2 \sqrt{375x^2\sqrt{3x^7}} \), if \( x \) is not equal to 0?

a. \( 15x^4 \sqrt{3x^7} \)
b. \( 40x^4 \sqrt{3x^7} \)
c. \( 15x^3 \sqrt{3x^7} \)
d. \( 40x^3 \sqrt{3x^7} \)

Answer 1

a. \( 15x^4 \sqrt{3x^7} \)

Step-by-step explanation:

To simplify the expression
`\( 8x^2 \sqrt{375x^2√(3x^7)} \), start by breaking down the radicals. \( 375 = 25 * 15 \) and \( x^2 = x * x \).`

The expression becomes
`\( 8x^2 \sqrt{25x^2 \cdot 15x^2√(3x^7)} \).Further simplifying gives \( 8x^2 \cdot 5x \cdot \sqrt{15x^2 √(3x^7)} \).`

Consolidating the constants results in
`\( 40x^3 \sqrt{15x^2 √(3x^7)} \).Now, simplify under the radical: \( 15x^2 = 3x \cdot 5x \) and \( √(3x^7) = √(3x^6) \cdot √(x) \).`

The expression is
`\( 40x^3 \cdot 5x \cdot √(3x^6) \cdot √(x) \), which simplifies to \( 200x^4 √(3x) \).`

Finally, this can be rewritten as \( 15x^4 \sqrt{3x^7} \), which matches option a.

Hence, the equivalent expression to \
`( 8x^2 \sqrt{375x^2√(3x^7)} \) is \( 15x^4 √(3x^7) \)`, matching choice a.