Question

The side length of a square is (√2-3√5) meters. Find the area of the square and write your answer in simplest radical form

Answer 1

47 - 6√10

Explanation:

Area of a square of side a = a²

Here a = √2 -3√5

Area A = a² = (√2 -3√5)²

We know that (a - b)² = a² -2ab +b²

So

A = (√2 -3√5)²

= (√2)² - 2(√2)(3√5) + (3√5)²

(√2)² = 2 because (√a)² = a

(3√5)² = 3² x (√5)² = 9 x 5 = 45

2(√2)(3√5) = 2 (√2 · 3 · √5)

= 2 x 3 √2 √5

√2√5 = √10

2 x 3 √2 √5 = 2 · 3 · √10 = 6√10

Therefore area = 2 - 6√10 + 45

= 47 - 6√10