Express (5+√3)2 in the form a + b √3 where a and b are integers?

Question

its 5 plus under root 3 then after bracket is square

Answer 1

If what you're asking for is... the square of [5 + (sqrt of 3)] then you would help yourself (and all us in answers) to present it this way: (5+√3)^2

That binomial squared is: 25 + 3 + 10[sqrt 3] which simplifies to

28 + 10 sqrt 3

[so your a = 28 and your b = 10.]

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In general when you square a binomial (2 term expression) you get 3 terms: the square of each term PLUS [twice the product of the 2 terms]. This last bracketed bit of typing is what careless math tends to omit.

e.g. 19^2 = [20 - 1]^2 = 400 + 1 - 40 = 361 (the correct way)

(a + b)^2 is NOT = a^2 + b^2;

but does equal a^2 + b^2 + 2ab (or rearranged...a^2 + 2ab + b^2)

Answer 2

= (5 + √3).(5 + √3)
= 25 + 10.√3 + 3
= 28 + 10√3

Answer 3

i think the answer is 28 + 10 under root 3,
a=28 b=10

5 square is 25, under root 3 square is 3 = 28

the remaining answer is the middle term being 5 under root 3 + 5 under root 3 = 10 under root 3

thus the answer 28 + 10 under root 3