Final answer:
To fully simplify the expression (5√-70)(√40), we simplify each square root individually and multiply the simplified forms together. The fully simplified expression is 100i√7.
Step-by-step explanation:
To fully simplify the expression (5√-70)(√40), we can start by simplifying each square root individually.
√-70 can be rewritten as √(-1)(√70). Since the square root of -1 is represented by the imaginary unit i, we have i√70.
√40 can be simplified as √(4)(√10), which gives us 2√10.
Now, we can multiply the simplified square roots: (5√-70)(√40) = 5(i√70)(2√10) = 10i√(70)(10) = 10i√700 = 10i√(100)(7) = 10i(10√7) = 100i√7.
The fully simplified expression is 100i√7.
Learn more about simplifying square roots