Answer:
c. 10√5
Step-by-step explanation:
To simplify the expression √10 × √50, we can combine the square roots under one radical and simplify the product.
1. First, let's simplify each square root separately:
- √10 cannot be simplified any further because 10 does not have any perfect square factors.
- √50 can be simplified as follows:
√50 = √(25 × 2) = √25 × √2 = 5√2
2. Now, let's substitute the simplified square roots back into the expression:
√10 × √50 = √10 × (5√2)
3. To multiply these square roots, we can multiply the coefficients (numbers outside the square root) and multiply the radicals (numbers inside the square root):
√10 × (5√2) = 5√(10 × 2) = 5√20
4. Finally, let's simplify the radical:
5√20 can be simplified as follows:
5√20 = 5√(4 × 5) = 5√4 × √5 = 5(2)√5 = 10√5
Therefore, the expression √10 × √50 simplifies to 10√5, which is option c.
