Emirandira gy'enamba

Gakuweebwa Charles Muwanga !! Emirandira gy’Ennamba (Roots of Numbers)

Mu Mirandira gya Namba mulimu:

a)	Emirandira gya kyebiriga.

Omulandira gwa kyebiriga era guyitibwa “omulandira ogw’okubiri” ogwa namba (the second root of a number).

b)	Emirandira gya kyesatuza.

Omulandira gwa kyesatuza era guyitibwa omulandira ogw’okusatu) ogwa namba.

c)	Emirandira gyonna egituuka ku namba “n”.

Emirandira egituuka ku “n” giyitibwa:

(a) Omulandira ogw’okuna ogw’ennamba era gulagibwa nga:  
 
(b) Omulandira ogw’okutaano ogw’ennamba era gulagibwa nga:  
N’okweyongerayo.

Emiramwa egyetaagisa okumanya ku mirandira gya namba:

(i)	Akabonero k’Omulandira (√). Buli mulandira gwa namba gulagibwa n’akabonero kano. Eky’okulabirako mu kikunizo √36, "√" ke kabonero k’omulandira.

(ii)	Ennandiko (radicand) ye namba eteekebwa wansi w’akabonero k’omulandira. Manya nti “ennandiko” ye namba eba munda mw’akabonero. Mu √36, "36” y’ennandiko.

(iii)	Enkubisa (coefficient) ye namba eri ku kabalaza k’akabonero k’omulandira. Mu kikunizo 3√8, "3” y’enkubisa.

(iv)	Omulandira ogutuuka ku “n” (“nth” root). Tobuzabuzibwa nkubisa na mulandira gutuuka ku “n” ("nth" root). Eky’okulabirako mu 3√27  kitegeeza 3 emirundi √27, naye  3√27  kitegeeza mulandira ogw’okusatu ogwa 27 oba kiyite omulandira gwa kyesatuza ogwa 27  oba omulandira ogw’okusatu ogutuuka ku 27 , olw’okuba 3 x 3 x 3  = 27, 3√27 = 3.)

(v)	Nambuluzo (factor) ye namba eyekubisibwamu okufuna namba endala oba okutuuka ku namba endala. Okufuna nambuluzo ky’okola kwe kugabiza mu namba ey’ensonga awatali nfikkizo. Eky’okulabirako 3 nambuluzo ya 12 kubanga 12÷ 4 = 3,   4 nambuluzo ya 16 kubanga 4 x 4 = 16.

(vi)	Okusonjola omulandira gwa kyebiriga (simplifying a square root). Okusonjola omulandira gwa kyebiriga kitegeeza okulambulula kyebiriga yonna entuukirivu okuva mu nandiko (radicand), okuzizza ku kkono w’akabonero k’omulandira n’okuleka nambuluzo endala munda mw’akabonero k’omulandira. Singa namba eba kyebiriga entuukirivu, kitegeeza akabonero k’omulandira kaba kaviirawo ddala ng’omaze okuwandiika omulandira. Eky’okulabirako √98 esonjolwa nga 7√2.

“Emirandira gy’Ennamba” explained in English

The Luganda word “omulandira” is the direct translation of the English word “root”, which has the same biological and mathematical meanings. Every tree has a root which supports it, absorbs water and nutrients from the soil. In number theory (omugereeso gw’ennamba), every “composite number” (ennamba ennambulukufu) has a “root” (omulandira).

Emirandira gya kyebiriga (square roots)

Omulandira gwa kyebiriga is also referred to as “omulandira ogw’okubiri” ogw’ennamba (the second root of a number)
Ennamba 1, 4, 9, 16, 25…… za kyebiriga, emirandira gyazo egya kyebiriga giba 1, 2, 3, 4, 5…….Kubanga singa okubisaamu buli emu emirundi ebiri ofuna enamba eza kyebiriga.

The shape above is called “kyebiriga” (square). “Kyebiriga” is calculated by multiplying a number two times. For example, if the number is n, when you multiply n x n, you get ekitondeko (product) n2, which is called “kyebiriga y’ennamba n” (the square of a number n). 

If we substitute (okusikiza) with 4, the square of four is 4 x 4 which is 42 = 16. You can see that the etymological meaning of kyebiriga, Luganda for “square” is in the number “bbiri” (two) because we get a square by multiplying the same number two times (emirundi ebiri). To “square a number” in Luganda is okubiriga or okwebiriga ennamba. You can even talk of “ennamba za kyebiriga” to mean “square numbers”. Doesn’t it make obvious sense to you?

When you have “ennamba ya kyebiriga” (a square number) like 4, its square root (omulandira gwa kyebiriga) is obviously 2. If ennamba ya kyebiriga is 16, its omulandira gwa kyebiriga (square root) is 4 and if you have ennamba ya kyebiriga 81, its omulandira gwa kyebiriga is 9.

Omulandira gwa Kyesatuza (Cube root).

“Omulandira gwa kyesatuza” is also referred to as “omulandira ogw’okusatu ogw’ennamba” (the third root of a number).

Ennamba 1, 8, 27, 64 …. za kyesatuza, emirandira gyazo egya kyesatuza giba 1, 2, 3, 4…. Kubanga singa wekubisaamu buli gumu emirundi esatu gwa ennamba za kyesatuza.

Enkula eva mu ekyo eba kyebiriga(Square shape)

Ebyokulabirako:

Singa ogambibwa nti webiriga 5 oba otegeesebwa kulaga taano nga 
52 = 5 x 5 = 25

At singa ogambibwa nti wesatuze 5 oba otegezebwa kulaga taano nga 
53 = 5 x 5 x 5 = 125