1. simplify the expression sqrt(4x^2/3y) show your work
2. simplify the expression (3-4i)(1+-i) show your work
3. the formula c=sqrt(a^2 + b^2) represents the length of the hypotenuse of a right triangle with side lengths a and b. solve the equation for b. show your work.

1. in this exercise, we need to simplify the expression:

the square root of a division equals the division of the square root sof the factors, thus:

and the square root of a product equals the product of the square roots of the factors as well, therefore:

2. we need to simplify the expression:

by applying distributive property we have:

3. for a right triangle we have:

squaring each side of the equation:

we have:

so, converting firstly the mixed fractions to improper fractions and then "adding".