In operations with the mathematical expressions containing square roots it is desirable to get rid of signs of the radical. There are two main methods to make it: calculation of value of a radicand or its simplification. The first option is applicable when under the sign of a root there are no unknown variables, and the second has no restrictions in use.
Instruction
1. If under the sign of a root there is a mathematical expression containing one or several variable values, then try to simplify it and to take out from under the radical. For example, if it is necessary to subtract a square root from expression 9*a²+9*b²+18*a*b, then its simplification will give more convenient set of two multipliers — 9 * (a+b)². The sign of the radical in this case can be removed after extraction of a root from each factor: √ (9*a²+9*b²+18*a*b) = √ (9 * (a+b)²) = 3 * (a+b). Then use the received expression in operation of subtraction instead of an initial square root.
2. If under the sign of the radical there is a numerical size, then calculation of value of a root with the subsequent subtraction of the received result will be the easiest way of the solution of a task. Having Internet access, it is very easy to make it, there is even no need to make any calculations. Pass, for example, on the website of the Google search engine and in a query field gather the necessary mathematical operation. Let's tell if it is required to subtract from number 5831 a square root from 563, then enter inquiry "5831 — sqrt 563". In this records reduction from the English name of a square root (SQuare RooT) replaces the sign of the radical. The calculator which is built in search engine will calculate and will display result even without pressing of the button of sending request for the server: 5,831 — sqrt(563) = 5 807.27238.
3. Use computing means of the operating system of your computer if Internet access is absent. It is the simplest to use in this case the program imitating the ordinary calculator. In Windows OS it is possible to start it through the main menu opened by click on the Start-up button — the corresponding reference is placed in its section "All Programs". After opening of the program gather number from which it is necessary to subtract a root, and press the M+ button in the interface of the calculator — so you place this value in his memory. Then enter number from which it is necessary to take a root, and click the button with the radical's badge (the second from above in the most right column) — the calculator will display the calculated value. Press button M - to subtract this size from the number placed in memory, and then by means of the MR button give the application the command to show result. The number which the calculator will display and will be result of subtraction of a square root.