Question

A square has an area of $4x^2+32x+64$ square units (x > 0). Write an expression for the side of the squre (in simplest form)

Answer 1

Let the side of the square is $y$ unit.

Then area of the square is $y^2$ square units.

Now,

$y^2=4x^2+32x+64$

$y^2=(2x{)}^2+2(2x\left)\right(8)+(8{)}^2$

$y^2={(2x+8)}^2$ [ $(a+b{)}^2=a^2+b^2+2ab$ ]

$y=\sqrt{{(2x+8)}^2}$

$y=|2x+8|$