Final answer:
To evaluate the expression 70/(√10+√20+√40 -√80), simplify the expression inside the parentheses to (3√10 - 2√5). Substituting this into the original expression gives 70/(3√10 - 2√5).
Step-by-step explanation:
To evaluate the expression 70/(√10+√20+√40 -√80), we first simplify the expression inside the parentheses. We can simplify the square roots by factoring out perfect squares from the radicand. Simplifying, we get: (√10+√20+2√10 -4√5).
Next, we combine like terms within the parentheses: (√10 + 2√10 + √20 - 4√5).
Finally, we add or subtract the terms within the parentheses to get the simplified expression: (3√10 - 2√5).
Substituting this simplified expression back into the original expression, we get: 70/(3√10 - 2√5).