I was tutoring a student on early trigonometry. Solving for the hypotenuse of a right triangle, but with sine, not Pythagoras.
The student went through getting the sine of a 45° triangle, and gave me the correct answer to 3 digits after decimal. (Note, the two legs of the triangle were both 7)
My issue – she had 0.7071 as sine of 45°, but lost the radical as she got the decimal solution. Her answer 7.071 was right, but I felt that $5\sqrt{2}$ was a missed opportunity. I accept and understand there‘s a time for calculators and 3 digits, but felt that early on, one should keep radicals, and both understand and be able to show the numbers for the sines of 0°, 30°, 45°, 60° and 90°.
The question - given that the US is going toward a common core approach, and given that students are allowed calculators early on, is there value to the pedagogical process to insist on keeping the irrational numbers through the solution? I am suggesting there will be greater understanding by keeping it, not indefinitely, but for understanding until the next level of math is introduced.