Final answer:
The value of the sequence square root of 2, square root of 2, square root of 2, square root of 2, square root of 2, square root of 2, square root of 2 is option b) square root of 2.
Step-by-step explanation:
The question asks about the value of a sequence where the same number, the square root of 2, is repeated seven times. To find the product of multiple instances of the same number, we raise that number to a power equal to the number of times it appears in the sequence.
Since we have the square root of 2 being multiplied by itself seven times, we can represent this as (sqrt(2))^7. Squaring a square root gives the original number, so (sqrt(2))^2 is 2. This property can help us simplify the expression.
The value of the sequence square root of 2, square root of 2, square root of 2, square root of 2, square root of 2, square root of 2, square root of 2 is square root of 2.
This is because all the terms in the sequence are equal to the square root of 2.
So the correct option is b) Square root of 2.