Question

Help asap!!! compute $\left(-3\sqrt{128}\right)\left(-4\sqrt{50}\right)$

Answer 1

960

Explanation:

We first simplify both square roots:\begin{align*}

\sqrt{128} &= \sqrt{64\cdot 2} = \sqrt{64}\cdot \sqrt{2} = 8\sqrt{2},\\

\sqrt{50} &= \sqrt{25\cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}.

\end{align*}Then, we have\begin{align*}

\left(-3\sqrt{128}\right)\left(-4\sqrt{50}\right) &= \left(-3\cdot 8\sqrt{2}\right)\left(-4\cdot 5\sqrt{2}\right)\\

&=\left(-24\sqrt{2}\right)\left(-20\sqrt{2}\right)\\

&=(-24)(-20)\left(\sqrt{2}\right)^2\\

&=480(2)\\

&=\boxed{960}.

\end{align*}

Answer 2

`(-3√(128))(-4√(50))\qquad \begin{cases} 128=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^6\cdot 2\\ \qquad (2^3)^2\cdot 2\\ 50=5\cdot 5\cdot 2\\ \qquad 5^2\cdot 2 \end{cases} \\\\\\ (-3√((2^3)^2\cdot 2))(-4√(5^2\cdot 2))\implies 12√((2^3)^2\cdot 2)\cdot √(5^2\cdot 2) \\\\\\ 12\cdot 2^3√(2)\cdot 5√(2)\implies 12\cdot 2^3\cdot 5\cdot √(2^2)\implies 12\cdot 2^3\cdot 5\cdot 2\implies 960`