Question

Simplify:

`(sqrt(2) + 1)^2`

Answer 1

Given: `(sqrt(2) + 1)^2`

Step wise calculation:

1. Expand the square using the formula (a + b)² = a² + 2ab + b²: 

`(sqrt(2) + 1)^2 = (sqrt(2))^2 + 2 xx sqrt(2) xx 1 + 1^2`

2. Calculate each term:

`(sqrt(2))^2 = 2`

`2 xx sqrt(2) xx 1 = 2sqrt(2)`

1² = 1

3. Sum the terms:

`2 + 2sqrt(2) + 1 = 3 + 2sqrt(2)`