Option B
[tex]3 x\sqrt{2} x[/tex] is the choice equivalent to [tex]\sqrt{6} x^{2} \cdot \sqrt{3} x[/tex]
Solution:
Step 1:
When we multiply two roots i.e. [tex]\sqrt{6} x^{2}[/tex] and [tex]\sqrt{3} x[/tex] the values are multiplied and still kept inside the root.
So [tex]\sqrt{6} x^{2}[/tex] × [tex]\sqrt{3} x[/tex] = [tex]\sqrt{6} x^{2} \times 3 x[/tex].
Step 2:
We then multiply the values in the root.
[tex]\sqrt{6} x^{2} \times 3 x[/tex] = [tex]\sqrt{18 x^{3}}[/tex]
Step 3;
We take the values out of the root by splitting up the value.
[tex]{18 x^{3}}[/tex] = [tex](9 \times 2)\left(x^{2} \times x\right)[/tex]
[tex]\sqrt{9}=3[/tex] and [tex]\sqrt{x^{2}}=x[/tex]
So [tex]\sqrt{18 x^{3}}[/tex] = [tex]\sqrt{9} \times 2 \times x^{2} \times x[/tex]
When we take values out of the root, we replace it with the square-rooted value on the outside.
[tex]\sqrt{18 x^{3}}[/tex] = [tex]3 x \sqrt{2 x}[/tex].
Thus option B is correct
