Question

True of false (sqrt 2 + sqrt 3)^2 =2+3=5

Answer 1

The answer is false

Answer 2

Answer: False

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Step-by-step explanation:

Recall that the FOIL rule says

`(a+b)^2 = (a+b)(a+b) = a^2+2ab+b^2`

If we plug in
`a = √(2)` and
`b = √(3)`, then you should find that

`(a+b)^2 = a^2+2ab+b^2\\\\(√(2)+√(3))^2 = (√(2))^2+2*√(2)*√(3)+(√(3))^2\\\\(√(2)+√(3))^2 = 2+2*√(2*3)+3\\\\(√(2)+√(3))^2 = 5+2√(6)\\\\`

So that 5 the student got is close, but there's a missing term needed to be added on: namely the
`2√(6)` term.