Question

What is the simplified form of 3√(x²+8xy+16y²) × 3√(x+4y)?

A. x(x+4y)
B. 3√(x+y)⁴
C. 3√(x+4y)⁴
D. 3√(x²+8xy+16y²)(x+4y)

Answer 1

The simplified form of 3√(x²+8xy+16y²) × 3√(x+4y) is 3√((x+4y)⁴).

Step-by-step explanation:

The simplified form of 3√(x²+8xy+16y²) × 3√(x+4y) is 3√((x+4y)⁴). To simplify the expression, we can combine the two cube roots by multiplying the constants outside the radicals and the expressions inside the radicals. The expression x²+8xy+16y² can be factored into (x+4y)², so we can rewrite the expression as 3√((x+4y)²) = 3√((x+4y)⁴).