Answer :
[tex] \sqrt{ x^{2} } = / x /, [/tex] where / x / is "the absolute value of x";
Then [tex] \sqrt{3 x^{2} } = \sqrt{3} / x / ;[/tex]
In ihe same way, [tex] \sqrt{3 x^{4} } = \sqrt{3} / x^{2} / = \sqrt{3} x^{2} ,[/tex]because [tex] x^{2} \geq 0 ;[/tex];
The square root of (3x^2) times 3 times the square root of (3x^4) is 9 × [tex]/ x /[/tex]×[tex] x^{2} [/tex] ;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[tex] x^{3} [/tex], for [tex]x \geq 0[/tex] and -3[tex] x^{3} [/tex], for [tex]x\ \textless \ 0 .[/tex]
Then [tex] \sqrt{3 x^{2} } = \sqrt{3} / x / ;[/tex]
In ihe same way, [tex] \sqrt{3 x^{4} } = \sqrt{3} / x^{2} / = \sqrt{3} x^{2} ,[/tex]because [tex] x^{2} \geq 0 ;[/tex];
The square root of (3x^2) times 3 times the square root of (3x^4) is 9 × [tex]/ x /[/tex]×[tex] x^{2} [/tex] ;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[tex] x^{3} [/tex], for [tex]x \geq 0[/tex] and -3[tex] x^{3} [/tex], for [tex]x\ \textless \ 0 .[/tex]
