Final answer:
The expression 8√10(8√5) simplifies to 64√50 using the properties of radicals and commutative property of multiplication.
Step-by-step explanation:
To simplify the given mathematical expression 8√10(8√5), we use the property of radicals that allows us to multiply the radicands (the numbers under the square root) when the roots are the same. In this case, both are square roots.
We can rewrite the given expression as 8 × √10 × 8 × √5.
Then, using the commutative property of multiplication, which states we can multiply numbers in any order, we can rearrange and group like terms together to get 8 × 8 × (√10 × √5). Multiplying 8 by 8 gives us 64.
The product of √10 and √5 gives us √(10 × 5), which simplifies to √50.
Therefore, the simplified form of the expression is 64√50.