Suppose that you had two squares, a small one and a large one. The area of the large square is twice that of the small square. How many times larger is the side length of the large square than the side length of the small square?

The side length of the large square is √2 times larger than the side length of the small square.

Step-by-step explanation:

Suppose we have a small square (square 1) and a large square (square 2). The area of the large square is twice that of the small square, that is,

A₂ = 2 A₁

A₂/A₁ = 2 [1]

The area of a square is equal to the length of the side (l) raised to the second power.

A = l²

l = √A

The ratio of l₂ to l₁ is:

l₂/l₁ = √A₂ / √A₁ = √ (A₂/A₁)

We can replace [1] in the previous expression.

l₂/l₁ = √2

The side length of the large square is √2 times larger than the side length of the small square.