Roots That Are Not Whole

x^2 = 5: no whole number squares to 5, but the equation still has two solutions. They are written with the radical sign: x = ±√5, the exact numbers whose squares are 5.

√5 is not a made-up dodge; it is a number a little over 2.2, living between √4 = 2 and √9 = 3. Exact answers keep the radical; a calculator can approximate it whenever a decimal is wanted.

So the root method never fails on x^2 = positive number: perfect squares give whole answers, the rest give radicals, and both are complete, correct solutions. What happens with a NEGATIVE number on the right is a different story, told two chapters from now.