I'm studying a Grade 10 maths book and was surprised to see the correct answer for this question was:
(/2 - 3x)(/3 + 2x) - /5x
= /6 + 2/2x - 3/3x - 6x - /5x
I thought it should be:
= /6 + 2x/2 - 3x/3 - 6x - /5x
I'm using this '/' symbol for the radical sign
Can you please help me understand why the variable x is placed inside the radical sign?
Thank you.
Summarizing comments above., by the commutative property of multiplication (which says that $a\times b = b\times a$ for any reals $a,b$) you have that:
$2\times x \times \sqrt{2} = 2\times \sqrt{2} \times x$
or, written with fewer multiplication signs but meaning the same thing:
$2x\times \sqrt{2} = 2\sqrt{2} ~x$
"can you help me understand why $x$ is placed inside the radical sign?"
$x$ does not go inside of the radical sign. Note the difference in meaning of $\sqrt{2x}=\sqrt{(2x)}$ and $\sqrt{2}~x=(\sqrt{2})~x$. The length of the horizontal bar of the radical denotes which terms following are included inside of the radical versus outside of the radical.