Use the Pythagorean theorem
Find the long side (hypotenuse) of a right triangle from the two shorter sides.
In a right triangle, the square of the longest side equals the sum of the squares of the other two: a² + b² = c². To find c, add the squares and take the square root.
Example: legs of 6 and 9. c = √(6² + 9²) = √117, which is about 10.8167.
Classic Graphing 84
Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.
Press 2nd and the x² key for the square-root symbol. Then type 6², +, 9² and close the bracket.
2nd√x²6x²+9x²)Press enter.
enter
You should see√(6²+9²) 10.81665383
Natural Scientific 991
Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.
Press the square-root key, then type 6² + 9². Press right to step out of the root and press =. The answer is shown in exact form.
√6x²+9x²▶=Press S⇔D to see it as a decimal.
S⇔D
You should see10.81665383
Classic CAS
Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.
Press ctrl and the x² key for the root. Open a bracket, type 6² + 9², close the bracket and press enter.
ctrl√x²(6x²+9x²)enter
You should see3·√13
The exact answer is 3√13. Press ctrl then enter instead of enter for a decimal.
RPN Scientific 15
Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.
Key in 6 and square it with g then x² (the g function above the √x key).
6gx²√xKey in 9, square it the same way, and add. Then press √x.
9gx²√x+√x
You should see10.8167
Tips
- To find a short side instead, subtract: a = √(c² − b²). Make sure the longest side is the one you start from.
- Square each side before adding. Adding first gives a wrong answer.