simplify
(3+3^1/2)((2+2^1/2))^2
To simplify the expression (3+3^1/2)((2+2^1/2))^2, we can start by simplifying the expressions within the parentheses.
First, let's simplify 3^1/2. The exponent 1/2 represents the square root. So, 3^1/2 is equal to the square root of 3.
Next, let's simplify 2^1/2. Similarly, 2^1/2 is equal to the square root of 2.
Now, let's substitute these simplified values back into the original expression:
(3+√3)((2+√2))^2
Next, let's simplify the expression within the second set of parentheses, (2+√2)^2. To square this expression, we multiply it by itself:
(2+√2)^2 = (2+√2)(2+√2)
To find the product, we can use the FOIL method, which stands for First, Outer, Inner, Last:
(2+√2)(2+√2) = 2*2 + 2*√2 + √2*2 + √2*√2
= 4 + 2√2 + 2√2 + 2
= 6 + 4√2
Now, let's substitute this simplified value back into the original expression:
(3+√3)(6 + 4√2)
To simplify further, we can distribute the terms:
3(6+4√2) + √3(6+4√2)
Using the distributive property:
= 18 + 12√2 + √3*6 + √3*4√2
Simplifying further:
= 18 + 12√2 + 6√3 + 4√2√3
Since √2√3 is the same as √(2*3), which simplifies to √6:
= 18 + 12√2 + 6√3 + 4√6
And that is the simplified form of the expression (3+3^1/2)((2+2^1/2))^2.