Why does 2 multiplied by root 2 equal to root 8?

When you multiply 2 by √2, you are essentially multiplying 2 by 2^(1/2). Using the properties of exponents, when you multiply two numbers with the same base, you add the exponents. Therefore, 2 * 2^(1/2) = 2^(1) * 2^(1/2) = 2^(1 + 1/2) = 2^(3/2). Simplifying this further, 2^(3/2) is equivalent to √(2^3) = √8.