To simplify the expression √5(10 – 4√2), we start by distributing the square root of 5 into the parentheses. This gives us:
√5 * 10 – √5 * 4√2.
Now, we can calculate each term:
- For the first term, √5 * 10 = 10√5.
- For the second term, √5 * 4√2 = 4 * √(5 * 2) = 4√10.
Putting it all together, the expression simplifies to:
10√5 – 4√10.
This is the simplified form of the original expression.