Final answer:
The square root of 289 is 17, which is the number that when squared equals 289.
Step-by-step explanation:
The student has asked for the square root of 289. We can approach this step by step. First, if we recall our perfect squares, we know that 17 squared (17²) is 289. Therefore, the square root of 289 (√289) is 17. This is because the square root operation essentially asks the question: 'Which number, when multiplied by itself, gives the original number?'
When you see a square root problem, it is often helpful to look for perfect square factors or if the number is itself a perfect square. In this case, 289 is a perfect square and its square root is an integer. Confirming that 17 is our answer, we can square 17 to check our work: 17 × 17 = 289. So, the square root of 289 is indeed 17.
To find the square root of 289, you can use a calculator or manually calculate it. Calculating manually, you need to factorize 289 into its prime factors and then pair them up. Since 17 * 17 = 289, the square root of 289 is 17.