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Nirina7
the answer:

radical number is sometimes called, irrational number. Radical number is inside the specific symbol √. For example,  √a is called square root of a, for all value positive of the number a. 
According to our case, there are five choices, among these, the numbers which can be called as radical are

3x√x²y ,  x√xy², 

proof:

 3x√x²y = √9x²x²y=  √9x²√x²y, and we know that √9x² = 3x, so √9x²√x²y= 3x√x²y

x√xy² =√x²xy² , and we know that √x² = x, so √x²√xy²= x√xy²

Radicals are irrational numbers and inside the square root the numbers are radical numbers. In the given option the like radicals are option a) and d).

Given :

[tex]2\sqrt{x^2y}[/tex]

Radicals are irrational numbers and inside the square root the numbers are radical numbers. In the given option the like radicals are:

a) [tex]3x\sqrt{x^2y}= \sqrt{(3x)^2x^2y}[/tex]

So, [tex]\sqrt{(3x)^2}= \sqrt{9x^2} = 3x[/tex]

[tex]\sqrt{(3x)^2x^2y} = 3x \sqrt{x^2y}[/tex]

Therefore, it is a radical.

b) [tex]-12x\sqrt{x^2y}[/tex]

minus sign indicates that it is not a radical.

c)  [tex]-2x\sqrt{xy^2}[/tex]

minus sign indicates that it is not a radical.

d)  [tex]x\sqrt{yx^2}=\sqrt{x^2yx^2}[/tex]

So, [tex]\sqrt{(x)^2}= x[/tex]

[tex]\sqrt{(x)^2x^2y} = x \sqrt{x^2y}[/tex]

Therefore, it is a radical.

e) [tex]-x\sqrt{x^2y^2}[/tex]

minus sign indicates that it is not a radical.

For more information, refer the link given below:

https://brainly.com/question/1369233

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