If p(x)= x^2 - 2root2x + 1, then p(3root2)= ?

19 - 2^(7/4)√3  or

13.174 to nearest thousandth.

Step-by-step explanation:

I am interpreting this as x^2 - 2√(2x) + 1

p(3√2) = (3√2)^2 - 2√(2*3√2) + 1

= 18 - 2√(6√2) + 1

= 19 - 2* √6 * 2^1/4

= 19 - 2*√2*√3*2^1/4

= 19 - 2^(7/4)√3.

=  13.174 to the nearest thousandth.

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus