Question

√162x^3(y^2)

Answer 1

\[√162x^3y^2\]

Answer 2

idk sorry

Answer 3

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Answer 4

Is this the problem?

\(\sqrt{162x^3y^2}\)

Answer 5

yes

Answer 6

the answer is \[9xy \sqrt{2x}\]

Answer 7

\(\sqrt{162x^3y^2}\)

\(= \sqrt{81 \times 2 \times x^2 \times x \times y^2}\)

\(= \sqrt{81}\sqrt{x^2y^2}\sqrt{2x}\)

\(= 9\sqrt{x^2y^2}\sqrt{2x}\)

The root of 81 is 9. That is simple.
The roots of 2 and x are irrational and stay inside the root. That is also simple.
The question is what to do with the roots of x^2 and y^2.

Answer 8

If the problem told you to assume the variables are non-negative, then

\(\sqrt{x^2} = x\)

and \(\sqrt{y^2} = y\)

If you were not told these variables are non-negative, then the roots are:

\(\sqrt{x^2} = |x|\)

and \(\sqrt{y^2} = |y|\)

Answer 9

If you were told the variables are non-negative, then you have:

\(= 9xy\sqrt{2x}\)

If you were not told the variables are non-negative, then the answer is:

\(= 9|xy|\sqrt{2x}\)