Square root of some number a call such number b that b² = a. Square roots from small numbers can be calculated in mind, for example √16 = 4, √81 = 9, √169 = 13. If it is necessary to calculate a root from larger numbers, then the computer facilities, for example, the calculator come to the rescue. How to be if there is a task to calculate a square root, for example, of four-digit number, and there is no calculator near at hand? There is a method allowing to take a square root from natural number with any number of figures.
Instruction
1. Let some number m = 213444 be given. It is necessary to find a root of this number. Let's break m from right to left into groups on two figures and we will designate them by m1, m2, m3, etc., at the same time if in number the odd number of figures, then in the first group there will be only one figure.m1 = 21 m2 = 34 m3 = 44B required result there will be so many figures how many groups will turn out as a result of splitting, in this case it will be some three-digit number T = _ _ _
2. Let's take the maximum figure a, such what a?? m1. Number a = 4 since 4 will be this number? = 16 <21. Figure a = 4, will be the first figure of required result, i.e. T = 4 _ _
3. Let's square the first figure of result of T and we will subtract result from the first group - m1, we will receive 21 - 4? = 5. Let's attribute number 5 to the second group at the left - m2, we will receive A = 534. Result of T we will increase the available part by 2, we will receive new value of number a = 8. Again we will take the maximum figure x, such that (ax) * x? A, where (ax) = 10 * a + x. It will be number 6 since 86 * 6 = 516 <534. Figure x = 6, will be the second figure of required result, i.e. T = 4 6 _
4. * x we will subtract the work (ax) from number A, we will attribute result to the third group at the left - m3 and we will designate by letter B, we will receive 534 - 86 * 6 = 534 – 516 = 18, B = (18m3) = 1844. Result of T we will increase the available part by 2, we will receive new value of number a = 92 (46 * 2). Let's take the maximum figure y, such that (ay) * y? B, where (ay) = 10 * a + y. It will be number 2 since 922 * 2 = 1844 = V.Tsifra y = 2, will be the third figure of required result, i.e. T = 4 6 2takim image, v213444 = 462