Question

The square root of (3x^2) times 3 times the square root of (3x^4)

Answer 1

$\sqrt{ x^{2} } = / x /,$ where / x / is "the absolute value of x";
Then $\sqrt{3 x^{2} } = \sqrt{3} / x / ;$
In ihe same way, $\sqrt{3 x^{4} } = \sqrt{3} / x^{2} / = \sqrt{3} x^{2} ,$because $x^{2} \geq 0 ;$;
The square root of (3x^2) times 3 times the square root of (3x^4) is 9 × $/ x /$×$x^{2}$ ;But, for x > 0, | x | = x ; for x < 0, | x | = –x ;
Finally, The square root of (3x^2) times 3 times the square root of (3x^4) is 3$x^{3}$, for $x \geq 0$ and -3$x^{3}$, for $x\ \textless \ 0 .$