The area of a square is 128x3y4 cm2. What is the length of one side of the square in simplest form

We know that the area of the square of side length L is:

A = L*L = L^2

In this case, we know that the area is:

A = 128*x^3*y^4 cm^2

Then we have:

L^2 = 128*x^3*y^4 cm^2

If we apply the square root to both sides we get:

√(L^2) = √( 128*x^3*y^4 cm^2)

L = √(128)*(√x^3)*(√y^4) cm

Here we can replace:

(√x^3) = x^(3/2)

(√y^4)  = y^(4/2) = y^2

Replacing these two, we get:

L = √(128)*x^(3/2)*y^2 cm

This is the simplest form of L.

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