Question

PLEASE SOLVE IT WITH EXPLANATION!!DONT TAKE POINTS :)​

Answer 1

$[Hello,BrainlyUser]$

Answer:

[A] $38+12\sqrt{10}$

Step-by-step explanation:

$\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2$

$=\left(2\sqrt{5}\right)^2+2\cdot \:2\sqrt{5}\cdot \:3\sqrt{2}+\left(3\sqrt{2}\right)^2$

$=38+12\sqrt{10}$

[CloudBreeze]

Answer 2

Step-by-step explanation:

We are asked to simply (2√5 + 3√2)². Using formula: (a + b)² = a² + b² + 2ab. Let's say 2√5 = a, 3√2 = b. So,

→ (a + b)² = a² + b² + 2ab

→ (2√5 + 3√2)² = (2√5)² + (3√2)² + 2(2√5)(3√2)

We are aware about the fact that root means 1/2 and square of root means 2/2 that is 1. Using this we get:

→ (2√5 + 3√2)² = 4(5) + 9(2) + 2(2√5)(3√2)

Solve the brackets, to do so first put the like terms in one box.

→ (2√5 + 3√2)² = 4(5) + 9(2) + 2(2*3)(√5)(√2)

Solve the rest calculations.

→ (2√5 + 3√2)² = 20 + 18 + 2(6)(√10)

→ (2√5 + 3√2)² = 38 + 12√10

Option (a) (38 + 12√10) is the correct option.