Kvadrat ildizlar jadvali

√a — kvadrati a ga teng bo'lgan MANFIY BO'LMAGAN son: √49 = 7, chunki 7² = 49. Manfiy sondan kvadrat ildiz chiqarilmaydi (haqiqiy sonlarda).

Ildiz butun chiqmasa, uni ko'paytuvchilarga ajratib soddalashtiriladi: √72 = √(36 · 2) = 6√2. Javobni DTM da aynan shu ko'rinishda yozish talab qilinadi.

Formulalar

Ko'paytmadan ildiz√(ab) = √a · √b (a, b ≥ 0)
Bo'linmadan ildiz√(a/b) = √a / √b (a ≥ 0, b > 0)
Ildiz ostidan chiqarish√(a²b) = a√b (a ≥ 0)
Kvadratdan ildiz√(a²) = |a|
Maxrajni ildizdan xalos qilish1/√a = √a / a

√n — uch xona aniqligida

n	√n	n	√n	n	√n	n	√n	n	√n
1	1,000	21	4,583	41	6,403	61	7,810	81	9,000
2	1,414	22	4,690	42	6,481	62	7,874	82	9,055
3	1,732	23	4,796	43	6,557	63	7,937	83	9,110
4	2,000	24	4,899	44	6,633	64	8,000	84	9,165
5	2,236	25	5,000	45	6,708	65	8,062	85	9,220
6	2,449	26	5,099	46	6,782	66	8,124	86	9,274
7	2,646	27	5,196	47	6,856	67	8,185	87	9,327
8	2,828	28	5,292	48	6,928	68	8,246	88	9,381
9	3,000	29	5,385	49	7,000	69	8,307	89	9,434
10	3,162	30	5,477	50	7,071	70	8,367	90	9,487
11	3,317	31	5,568	51	7,141	71	8,426	91	9,539
12	3,464	32	5,657	52	7,211	72	8,485	92	9,592
13	3,606	33	5,745	53	7,280	73	8,544	93	9,644
14	3,742	34	5,831	54	7,348	74	8,602	94	9,695
15	3,873	35	5,916	55	7,416	75	8,660	95	9,747
16	4,000	36	6,000	56	7,483	76	8,718	96	9,798
17	4,123	37	6,083	57	7,550	77	8,775	97	9,849
18	4,243	38	6,164	58	7,616	78	8,832	98	9,899
19	4,359	39	6,245	59	7,681	79	8,888	99	9,950
20	4,472	40	6,325	60	7,746	80	8,944	100	10,000

Savol va javob

√72 ni qanday soddalashtiriladi?

To'liq kvadratni ajratiladi: √72 = √(36 · 2) = 6√2.

√(a²) nimaga teng?

|a| ga, ya'ni a ning moduliga. √((−5)²) = 5, −5 emas.

Manfiy sondan ildiz chiqadimi?

Haqiqiy sonlarda yo'q: hech bir sonning kvadrati manfiy emas.