Final answer:
To write the expression 12 + √128 1-√√√2 in the form a + b√2, simplify the terms and separate them. Simplify √128 as 8√2, and simplify √√√2 as 1 - 2^(1/16). Then, put these simplified terms together.
Step-by-step explanation:
To write the expression 12 + √128 1-√√√2 in the form a + b√2, we need to simplify it and separate the terms.
For the first term, 12 + √128, we can simplify √128 as √(64 * 2), which becomes 8√2. So, we have 12 + 8√2.
For the second term, 1-√√√2, we need to simplify the nested square roots. Simplifying √√√2 results in √(√(√2)), which is equivalent to √(2^(1/8)), or 2^(1/16). So, we have 1 - 2^(1/16).
Putting these simplified terms together, we have the expression in the form a + b√2 as 12 + 8√2 + (1 - 2^(1/16)).
Learn more about simplifying square roots