What are two square roots of ten?
+ and - 3.162278..
well, I think you mean
what are two solutions to
something^2 = 10
that something could be square root of ten which is about
3.16227766 etc
BUT it could also be
-3.16227766 etc
because negative times negative is positive
-3 times -3 is 9
just like
+3 times +3 is 9
To find the square roots of ten, we can use a calculator or perform the calculation manually.
1. Using a Calculator:
- Open a calculator app or use the calculator on your device.
- Enter 10.
- Press the square root (√) button, usually denoted by √ or sqrt.
- The calculator will display the square root of ten, which is approximately 3.16227766.
2. Manual Calculation:
To find the square roots of ten manually, we can use the square root approximation method.
- Start by making an initial guess. Since 4^2 = 16 and 3^2 = 9, we can assume that the square root of 10 lies between 3 and 4.
- Choose a value between 3 and 4. For example, let's take 3.5 as our initial approximation.
- Divide 10 by the approximation: 10 ÷ 3.5 = 2.857142857
- Average the approximation with the result of the division: (3.5 + 2.857142857) ÷ 2 = 3.178571429
- Repeat the previous two steps a few more times to get a more accurate approximation:
- 10 ÷ 3.178571429 = 3.149162794
- (3.178571429 + 3.149162794) ÷ 2 = 3.163867111
- 10 ÷ 3.163867111 = 3.162455622
- (3.163867111 + 3.162455622) ÷ 2 = 3.162661366
- Continue this process until you've reached your desired level of accuracy. In this case, we can round to two decimal places.
- Finally, the square root of 10 is approximately 3.16.
Hence, the two square roots of ten are approximately:
- √10 ≈ 3.16 (positive square root)
- -√10 ≈ -3.16 (negative square root)