Question

simplify the square root of 8x^3

Answer 1

\[\Large \sqrt{8x^3}\]


\[\Large \sqrt{4*2*x^2*x}\]


\[\Large \sqrt{4}*\sqrt{2}*\sqrt{x^2}*\sqrt{x}\]


\[\Large 2*\sqrt{2}*x*\sqrt{x}\]


\[\Large 2x\sqrt{2x}\]


So \[\Large \sqrt{8x^3}=2x\sqrt{2x}\] for all nonnegative values of x.

Answer 2

We have \[\sqrt{8x^3}\]
We know
\[8=2\times 2 \times 2\]
and
\[x^3=x \times x \times x\]
so we have
\[\sqrt {8x^3}=\sqrt{2\times 2 \times 2 \times x \times x \times x}\]
or
\[\sqrt{2^2 \times 2 \times x^2 \times x}\]
so
we get
\[2x\sqrt{2x}\]