Question

http://prntscr.com/1zxqcq

Answer 1

\(\bf \sqrt{3x^2}\cdot \sqrt{4x}\implies \sqrt{3x^2\cdot 4x}\implies \sqrt{12x^2}\\ \quad \\
\color{blue}{12\implies 2\times 2\times 3\implies 2^2\times 3}\\ \quad \\
\sqrt{12x^2}\implies \sqrt{2^2\times 3}\)

Answer 2

\(\bf \sqrt{3x^2}\cdot \sqrt{4x}\implies \sqrt{3x^2\cdot 4x}\implies \sqrt{12x^2}\\ \quad \\
\color{blue}{12\implies 2\times 2\times 3\implies 2^2\times 3}\\ \quad \\
\sqrt{12x^2}\implies \sqrt{2^2\times 3\times x^2}\)

Answer 3

thank you i got C is that correct?

Answer 4

Not quite, but close.

Answer 5

Actually jdoe made a mistake, he missed an x at the last step of the first line. it's supposed to be x to the 3rd power

Answer 6

\[\sqrt{3*x^2*4*x} = \sqrt{12*x^3}\]

Answer 7

We keep losing an x.

\(\sqrt{3x^{2}}\cdot\sqrt{4x}\)

Since we have that x by itself in the second radical, we now know that x is NOT negative!! This is good news.

\(\sqrt{3}\sqrt{x^{2}}\cdot\sqrt{4}\sqrt{x}\)

Pick off the easy one.

\(\sqrt{3}\sqrt{x^{2}}\cdot 2 \sqrt{x}\)

We now use the fact that \(x \ge 0\)

\(\sqrt{3} \;x\cdot 2 \sqrt{x}\)

Rearrange a little:

\(2x\sqrt{3}\sqrt{x} = 2x\sqrt{3x}\)

Answer 8

technically \[2*\left| x \right|*\sqrt{3*x}\]

Answer 9

Technically, no. \(\sqrt{x^{2}} = x\) IF you know that \(x \ge 0\), which we do in this case. Had \(\sqrt{4x}\) not appeared separately, we would not have known that. Absolute values are not required in this case.