find the simplified product where $xgeq0$: $sqrt{5x}(sqrt{8x^{2}} - 2sqrt{x})$ \n$sqrt{10x}$\n$2xsqrt{40x}-2x…

find the simplified product where $xgeq0$: $sqrt{5x}(sqrt{8x^{2}} - 2sqrt{x})$ \n$sqrt{10x}$\n$2xsqrt{40x}-2x$\n$2xsqrt{10x}-2sqrt{5x}$\n$2xsqrt{10x}-2xsqrt{5}$

find the simplified product where $xgeq0$: $sqrt{5x}(sqrt{8x^{2}} - 2sqrt{x})$ \n$sqrt{10x}$\n$2xsqrt{40x}-2x$\n$2xsqrt{10x}-2sqrt{5x}$\n$2xsqrt{10x}-2xsqrt{5}$

Answer

Explanation:

Step1: Distribute $\sqrt{5x}$

$\sqrt{5x}\times\sqrt{8x^{2}}-\sqrt{5x}\times2\sqrt{x}$

Step2: Use the product - rule of square roots $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$

For $\sqrt{5x}\times\sqrt{8x^{2}}$, we have $\sqrt{5x\times8x^{2}}=\sqrt{40x^{3}}$. For $\sqrt{5x}\times2\sqrt{x}$, we have $2\sqrt{5x\times x}=2\sqrt{5x^{2}}$.

Step3: Simplify the square - roots

$\sqrt{40x^{3}}=\sqrt{4x^{2}\times10x}=2x\sqrt{10x}$ and $2\sqrt{5x^{2}} = 2x\sqrt{5}$

Answer:

$2x\sqrt{10x}-2x\sqrt{5}$