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# expand (4+3√2)^2?

give your answer in the form a + b √2 where a and b are integers

### 7 Answers

- JimLv 72 months ago
Use FOIL (a+b)(c+d) = ac+ad+bc+bd

(4+3√2)(4+3√2) = 16 + 12√2 + 12√2 +9*2

add like items

34 + 24√2

- Engr. RonaldLv 72 months ago
(4+3√2)^2

=(4+3√2)(4+3√2)

=16 + 12√(2) + 12√(2) + 9√(4)

=16 + 24√(2) + 9 * 2

=16 + 24√(2) + 18

=34 + 24√(2) Answer//

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- llafferLv 72 months ago
It's the same as this general form:

(x + y)² = x² + 2xy + y²

where:

x = 4

y = 3√2

So this turns into:

(4 + 3√2)² = 4² + 2(4)(3√2) + (3√2)²

Now simplify the right side:

(4 + 3√2)² = 16 + 24√2 + 9 * 2

(4 + 3√2)² = 16 + 24√2 + 18

(4 + 3√2)² = 34 + 24√2

Testing both sides by using √2 = 1.41421:

(4 + 3√2)² = 34 + 24√2

(4 + 3 * 1.41421)² = 34 + 24 * 1.41421

(4 + 4.24263)² = 34 + 33.94104

8.24263² = 67.94104

67.9409493169 = 67.94104

round each to 5SF to get:

67.941 = 67.941

TRUE

So this is correct. The simplified expansion is:

(4 + 3√2)² = 34 + 24√2

- la consoleLv 72 months ago
= (4 + 3√2)² → recall: (a + b)² = a² + 2ab + b²

= (4)² + 2.(4 * 3√2) + (3√2)²

= 16 + 24√2 + 18

= 34 + 24√2