square root 2 (square root 10+8 square root2)

To simplify the expression √2(√10 + 8√2), we can distribute the square root of 2 to each term inside the parentheses.

√2(√10 + 8√2) = √2 * √10 + √2 * 8√2

To multiply square roots, we can combine the numbers inside the square root and simplify.

√2 * √10 = √(2 * 10) = √20

√2 * 8√2 = 8√(2 * 2) = 8√4 = 8 * 2 = 16

Now we can rewrite the expression as:

√20 + 16

The square root of 20 can be further simplified by finding the largest perfect square that divides 20, which is 4.

√20 = √(4 * 5) = √4 * √5 = 2√5

Finally, we substitute this simplified value back into the expression:

2√5 + 16

Therefore, the simplified form of √2(√10 + 8√2) is 2√5 + 16.