# expand (4+3√2)^2?

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

Relevance
• Jim
Lv 7
1 month ago

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

34 + 24√2

• ?
Lv 7
2 months ago

[4+3sqr(2)]^2

=

16+24sqr(2)+18

=

34+24sqr(2)

=>

a=34

b=24

• 2 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

• 2 months ago

(4 + 3√2)^2 = 34 + 24√2

• 2 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

• 2 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

• David
Lv 7
2 months ago

It is: 18 + 8 times square root 2