Question

Simplify each expression. Rationalize all denominators. Assume that all variables are positive.
1) square root of 200x^3y over square root of 2xy^5
2) (8-3square root of 2)(8+3square root of 2)

Please explain and show steps!

Answer 1

Ist the numerator

\[\sqrt{200x^3y} = \sqrt{2 \times 100 \times x^2 \times x \times y} = \sqrt{100x^2}\times \sqrt{2xy}\]

this simplifes to
\[10x \sqrt{2xy}\]

now the denominator

\[\sqrt{2xy^5} = \sqrt{y^4} \times \sqrt{2xy}\]

which simplifes to

\[y^2 \sqrt{2xy}\]

the problem is now

\[(10x \sqrt{2xy})/(y^2 \sqrt{2xy})\]

cancelling common factors gives

\[10x/y^2\]

Answer 2

what does Rationalize all denominators mean?

Answer 3

@campbell_st do you know how to do (8-3square root of 2)(8+3square root of 2)

Answer 4

This ia a binomial expansion called the difference of two squares


\[(8 - 3\sqrt{2})(8 + 3\sqrt{2})\]

then answer is

\[8^2 - (3\sqrt{2})^2 = 64 - 9\times2\]

I'll let you finish it