Question

Express in simplest radical form.

5x√192x³+√3x5

please help!!

Answer 1

`-5x√(192x^3) + √(3x^5)\\\\=-5x\left(192x^3 \right)^(\tfrac 12) + \left(3x^5 \right)^(\tfrac 12)\\\\=-5\cdot (192)^(\tfrac 12) \cdot x \cdot x^(\tfrac 32) + 3^(\tfrac 12) \cdot x^(\tfrac 52)\\\\=-5\left( 64 \cdot 3 \right)^(\tfrac 12) \cdot x^(1+\tfrac 32) + 3^(\tfrac 12) \cdot x^(\tfrac 52)\\\\=-5\cdot 8\cdot 3^(\tfrac 12) \cdot x^(\tfrac 15) + 3^(\tfrac 12) \cdot x^(\tfrac 52)\\\\=-40\cdot 3^(\tfrac 12) \cdot x^(\tfrac 52)+3^(\tfrac 12) \cdot x^(\tfrac 52)\\\\`

`=-39\cdot 3^(\tfrac 12) \cdot x^(\tfrac 52)\\\\=-39\sqrt 3 √(x^5)`