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) } = √(3) / x / ;`
In ihe same way,
`\sqrt{3 x^(4) } = √(3) / x^(2) / = √(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 .`