Question

Find the area of a square with a side of length 2 Square root of 3+6 square root of 7 inches

Answer 1

(264+24√21) in²

Explanation:

Area of a square = Length * Length

A = L²

Given the length of a square as
`2√(3)+6√(7)` inches' The area of the square will be calculated as shown;

`A = (2√(3)+6√(7))^2\\\\A = (2√(3)+6√(7))(2√(3)+6√(7))\\\\A =(2√(3))(2√(3))+(2√(3))(6√(7))+(6√(7))(2√(3))+(6√(7))(6√(7))\\\\A = 4√(9)+12√(21)+12√(21)+36√(49)\\\\A = 4(3)+24√(21)+36(7)\\ \\A = 12+24√(21)+252\\\\A = 264+24√(21)`

Hence the area of the square is (264+24√21) in²