How do you represent under root of 6 on a number line with justification?

To represent √6 on a number line, first identify the integers it lies between, which are 2 and 3, since 2² = 4 and 3² = 9. Next, approximate its value; √6 is about 2.45. You can use a compass to find the exact point by constructing a right triangle with legs of length 2 and √2 (the distance from 2 to √6) to pinpoint its location accurately on the number line. This confirms that √6 is approximately 2.45, positioned slightly closer to 2.5 than to 2.