Simplify (2√5+3√7)^2 Show your work. Justify each step.

Answer 1

(2√5+3√7)^2

Step 1: Expand using the distributive property
= (2√5+3√7)(2√5+3√7)

Step 2: Use the FOIL method to multiply the two binomials
= 4(√5)^2 + 6√5√7 + 6√5√7 + 9(√7)^2

Step 3: Simplify the terms inside the parentheses
= 4(5) + 12√35 + 9(7)

Step 4: Simplify further
= 20 + 12√35 + 63

Step 5: Combine like terms
= 83 + 12√35

Therefore, (2√5+3√7)^2 simplifies to 83 + 12√35.