00:01
This problem says the area of a rectangle is 12 centimeters squared and the length is 2 plus square to 7.
00:06
Find the width in the form of a plus b times square to 7 where a and b are integers.
00:10
So even though we have a complex conjugate expression with a radical, we still know that area of a rectangle is length times width.
00:18
So we have our length of 2 times square to 7.
00:22
That is multiplied by whatever w is to give us 12 centimeters squared.
00:27
So if we want to solve for the w, we can just divide by 2 .2.
00:30
Plus square root of seven on both sides.
00:35
And when we get that our w is equal to 12 over 2 plus square root of 7, that is technically accurate, but that is not rationalized because we have a radical in the bottom of the fraction.
00:44
So we'll begin to rationalize it and we'll see if we have an answer that turns into the form of a plus b times square root of 7.
00:51
So to rationalize, since we have an expression on bottom, we can't just multiply by square of 7.
00:56
We have to multiply by the conjugate, which is 2 n squared of 7 to make...