Simplify: (2^1/2) * (8^1/2)/4
(2^1/2) * (8^1/2)/4
= (2^1/2) * (8^2)
= (2^1/2) * (2^3)2
= 2^(1/2) * 2^6
= 2^(6.5) or 2^(13/2) or (√2)^13
To simplify the given expression, we can follow these steps:
Step 1: Simplify the exponents inside the parentheses.
2^(1/2) can be written as the square root of 2.
8^(1/2) can be written as the square root of 8.
So the expression becomes:
(√2 * √8)/4
Step 2: Simplify the square roots.
√2 = √(2*1) = √2 * √1 = √2
√8 = √(4*2) = √4 * √2 = 2 * √2
Now the expression becomes:
(2 * √2 * 2 * √2)/4
Step 3: Simplify the expression further.
Combining like terms, we get:
(2 * 2 * 2 * √2 * √2)/4
This simplifies to:
(8 * 2 * √2 * √2)/4
Step 4: Simplify the expression to its final form.
The square roots of 2 multiplied by themselves give us 2. So, we have:
(8 * 2 * 2)/4
Multiplying the numbers, we get:
(32 * 2)/4
Dividing 32 by 4, we get:
64/4
Finally, simplifying the expression:
16
So, the simplified solution is 16.