To simplify the expression √10 * √8, you can use the property of square roots that states √a * √b = √(a * b).
1. **Combine the square roots**: Start by combining the two square roots:
√10 * √8 = √(10 * 8)
2. **Perform the multiplication inside the square root**: Calculate the product of 10 and 8:
10 * 8 = 80
Now your expression looks like this:
√80
3. **Simplify √80**: Next, we want to simplify √80 further. To do that, we can factor 80 into its prime factors:
80 = 16 * 5
Since 16 is a perfect square (4 * 4), we can take the square root of it:
√80 = √(16 * 5) = &radic{16} * &radic{5}
4. **Taking the square root**: Now calculate the square root of 16:
√16 = 4
So, you have:
√80 = 4 * &radic{5}
5. **Final result**: Thus, the simplified form of √10 * √8 is:
4 √5
In summary, the simplified expression for the square root of 10 multiplied by the square root of 8 is 4 √5.