Question

What is the product? Assume x greater-than-or-equal-to 0 (StartRoot 3 x EndRoot + StartRoot 5 EndRoot) (StartRoot 15 x EndRoot + 2 StartRoot 30 EndRoot) 3 x StartRoot 5 EndRoot + 3 StartRoot 165 x EndRoot + 10 StartRoot 6 EndRoot 3 x StartRoot 5 EndRoot + 6 StartRoot 10 x EndRoot + 5 StartRoot 3 x EndRoot + 10 StartRoot 6 EndRoot 3 x StartRoot 5 EndRoot + 10 StartRoot 6 EndRoot StartRoot 3 x EndRoot + 5 StartRoot 3 x EndRoot + 10 StartRoot 6 EndRoot

Answer 1

Answer:

  3x√5 + 6√(10x) + 5√(3x) + 10√6

Step-by-step explanation:

  $(\sqrt{3x}+\sqrt{5})(\sqrt{15x}+2\sqrt{30})=\sqrt{3x}(\sqrt{15x}+2\sqrt{30})+\sqrt{5}(\sqrt{15x}+2\sqrt{30})\\\\=\sqrt{45x^2}+2\sqrt{90x}+\sqrt{75x}+2\sqrt{150}\\\\=\sqrt{5(3x)^2}+2\sqrt{10x(3)^2}+\sqrt{3x(5)^2}+2\sqrt{6(5)^2}\\\\=\boxed{3x\sqrt{5}+6\sqrt{10x}+5\sqrt{3x}+10\sqrt{6}}$

__

The applicable rules of roots are ...

  (√a)(√b) = √(ab)

  √(ab²) = b√a