In mathematical tasks such expression as a root square of a square sometimes meets. As squaring and extraction of a square root – function the mutually return, some just "reduce" them, rejecting the sign of a root and square. However such simplification is not always correct and can result in incorrect results.
It is required to you
- calculator
Instruction
1. To find a root square numbers, specify the sign of this number. If number non-negative (positive or zero), then the root of a square is equal to the most this number. If the squared number negative, then the root square of its square is equal to the opposite number (increased by-1). This rule can be formulated well: the root of a square of number is equal to this number without sign. In the form of a formula this rule looks even more simply: kh² = |x|, where |x| - module (absolute value) of number x. For example: √10² = 10,√0² = 0, √ (-5)² = 5.
2. To find a root of a square of numerical expression, previously count value of this expression. Depending on the sign of the turned-out number, act as it is described in the previous point. For example: √ (2-5)² = √ (-3)² = 3esli it is necessary to show not result, but an operations procedure, the squared numerical expression can return an initial form: √ (2-5)² = √ (-3)² = 3 = - (2-5), or √ (2-5)² = √ (-3)² = 3 = 5-2
3. For finding of a root from an expression square with the parameter (variable numerical value), it is necessary to find areas of positive and negative values of expression. To define these values, define the corresponding values of parameter. For example, it is necessary to simplify expression: √(п-100)², where p – the parameter (number unknown in advance). Find at what values p: (p-100) <0. It turns out that at p <100. Therefore: √(п-100)² = p-100 at p ≥100 and √ (p-100)²=100-п at p <100.
4. The answer form for a problem of finding of a root from a square shown above though is classical at the solution of school tasks, is pretty bulky and is not absolutely convenient in practice. Therefore, at extraction of a root of expression, square from a square, for example, in Excel just leave all expression in an initial look: = ROOT (DEGREE ((B1-100); 2)), or transform it to expression of type: =ABS(B1-100), where B1 – the address of a cage in which the value of the p parameter from the previous example is kept. The second option is more preferable as allows to achieve the bigger accuracy and speed of calculations.