A square picture frame occupies an area of 112 ft^2. What is the length of each side of the picture in simplified radical form?

Question

anonymous · Answer

the length of each side of the picture is 112^(1/2) = 4v7

anonymous · Answer

Whats the v

whpalmer4 · Answer

That's the lazy way of writing 

$$\sqrt{112} = 4\sqrt{7}$$
Area of a square = length * width = length * length
$$A = 112 ft^2 = L*L$$
$$L = \sqrt{112 ft^2}$$
That means that we need to find the square root of 112, which we can simplify by factoring and pulling out pairs of identical factors.
$$112 = 2*56 = 2*2*28 = 2*2*2*14 = 2*2*2*2*7$$
$$\sqrt{112} = \sqrt{(2*2)*(2*2)*7} = 2*2\sqrt{7} = 4\sqrt{7}$$

anonymous · Answer

Thank you for explaining it to me.

whpalmer4 · Answer

Say the picture frame has an area of 200 ft^2, what is the length of each side?  We'll test how well the explanation worked :-)