18/3square roots of 6-7square roots of 2
To simplify the expression 18 / (3√6 - 7√2), we need to rationalize the denominator. Rationalizing involves getting rid of any irrational numbers in the denominator (in this case, square roots).
Here are the steps to simplify the expression:
Step 1: Distribute the negative sign across the terms in the denominator:
18 / (3√6 - 7√2) = 18 / 3√6 + 7√2
Step 2: Simplify the expression by dividing both the numerator and the denominator by the common factor, which is 3:
18 / 3√6 + 7√2 = 6 / √6 + 7√2
Step 3: Rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator, which is √6 - 7√2:
(6 / √6 + 7√2) * (√6 - 7√2) / (√6 - 7√2)
= (6√6 - 42) / (6 - 98)
Step 4: Simplify the denominator:
= (6√6 - 42) / -92
So, the final simplified expression is:
18 / (3√6 - 7√2) = (6√6 - 42) / -92