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.