
Doug C. answered 06/11/24
Math Tutor with Reputation to make difficult concepts understandable
The square root of 10 is a number when multiplied times itself gives a result of 10.
Since 3 times 3 = 9, and 4 times 4 = 16, the number we are looking for is between 3 and 4, seemingly much closer to 3 than 4.
3.1 times 3.1 = 9.61
3.2 times 3.2 = 10.24
Now we know the number is between 3.1 and 3.2, perhaps a little closer to 3.2 than 3.1.
3.162=9.9856
3.172=10.0489
There is actually an algorithm that can be used to calculate square roots, but with calculators being so readily available...
√10 ≈ 3.16227766017 (that is an approximate value) The square root of 10 is called an irrational number. It's decimal equivalent goes on forever without repeating.
The number 10 actually has two square roots, one positive and one negative.
-√10 ≈ -3.16227766017
Hopefully you know how to get the approximate value using a calculator. The square root function on a TI-83(84) is located above the x2 key. So, 2nd - x2 - 10 - enter is the sequence.

Doug C.
desmos.com/calculator/vp3bbdnih806/11/24