Express (8 - 3sqrt(2))/(4 + 3sqrt(2)) in the form of a + b * sqrt(2) where a and b are integers.

The expression is in the form where a = -25 and b = 18

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Work Shown:

Let and then square both sides

We'll use both x and x^2 later on.

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The denominator is in the form 4+x. We'll multiply top and bottom by 4-x to then use the difference of squares rule. This will allow us to eliminate the square root in the denominator.

Therefore,

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Checking the

Use a calculator to find that,

We get the same decimal approximation, which helps confirm the correct answer.

Or you could use the idea that if M = N, then M-N = 0 to subtract the original expression M and the final result N. You should get 0 or very close to it.

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let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.