Lub hauv paus cim (√) sawv cev rau lub hauv paus cag ntawm tus lej. Koj tuaj yeem pom lub hauv paus cim hauv algebra lossis txawm tias siv ntoo lossis lwm yam haujlwm uas cuam tshuam nrog geometry lossis suav qhov txheeb ze qhov sib txawv lossis nrug. Yog tias cov hauv paus tsis muaj qhov ntsuas zoo ib yam, koj tuaj yeem hloov qhov sib npaug kom txog thaum qhov ntsuas tau zoo ib yam. Yog tias koj xav paub yuav ua li cas muab cov hauv paus hniav nrog lossis tsis muaj kev sib koom ua ke, tsuas yog ua raws cov theem no.
Kauj ruam
Txoj Kev 1 ntawm 3: Muab Cov Hauv Paus Loj Tsis Muaj Coefficients
Kauj Ruam 1. Ua kom ntseeg tau tias cov hauv paus hniav muaj qhov ntsuas zoo ib yam
Txhawm rau muab cov hauv paus hniav siv cov txheej txheem yooj yim, cov hauv paus no yuav tsum muaj qhov ntsuas ib yam. "Index" yog tus lej tsawg heev, sau nyob rau sab saud sab saud ntawm kab hauv lub cim hauv paus. Yog tias tsis muaj tus lej lej, lub hauv paus yog lub hauv paus square (index 2) thiab tuaj yeem muab sib ntxiv los ntawm lwm lub hauv paus cag. Koj tuaj yeem muab cov hauv paus hniav los ntawm qhov ntsuas sib txawv, tab sis txoj hauv kev no nyuaj dua thiab yuav piav qhia tom qab. Nov yog ob qho piv txwv ntawm kev sib npaug siv cov hauv paus nrog tib qhov ntsuas:
- Piv txwv 1: (18) x (2) =?
- Piv txwv 2: (10) x (5) =?
- Piv txwv 3: 3(3) xwm 3√(9) = ?
Kauj Ruam 2. Muab cov zauv hauv qab hauv paus cag
Tom ntej no, tsuas yog muab cov lej uas nyob hauv qab lub hauv paus cag los yog kos npe thiab tso nws rau hauv qab lub hauv paus plaub fab. Nov yog koj ua nws li cas:
- Piv txwv 1: (18) x (2) = (36)
- Piv txwv 2: (10) x (5) = (50)
- Piv txwv 3: 3(3) xwm 3√(9) = 3√(27)
Kauj Ruam 3. Yooj yim rau kev qhia hauv paus
Yog tias koj muab cov hauv paus hniav ntau ntxiv, nws muaj peev xwm tias cov txiaj ntsig tuaj yeem ua kom yooj yim rau lub xwmfab zoo lossis cov cubic zoo meej, lossis qhov txiaj ntsig tuaj yeem yooj yim los ntawm kev nrhiav lub xwmfab zoo meej uas yog qhov tseem ceeb ntawm cov khoom. Nov yog koj ua nws li cas:
- Piv txwv 1: (36) = 6. 36 yog lub xwmfab zoo tshaj plaws vim tias nws yog cov khoom ntawm 6 x 6. Lub hauv paus ntawm 36 tsuas yog 6.
-
Piv txwv 2: (50) = (25 x 2) = ([5 x 5] x 2) = 5√ (2). Txawm hais tias 50 tsis yog lub xwmfab zoo meej, 25 yog qhov tseem ceeb ntawm 50 (vim nws faib 50 tus tusyees) thiab yog lub xwmfab zoo meej. Koj tuaj yeem tsoo 25 rau hauv nws qhov tseem ceeb, 5 x 5, thiab coj ib qho 5 tawm ntawm cov cim hauv paus cag kom yooj yim qhia.
Koj tuaj yeem xav txog nws zoo li no: Yog tias koj tso 5 rov qab rau hauv paus, nws sib npaug nws tus kheej thiab rov qab mus rau 25
- Piv txwv 3:3(27) = 3. 27 yog lub cubic zoo vim nws yog cov khoom ntawm 3 x 3 x 3. Yog li, cov hauv paus cag ntawm 27 yog 3.
Txoj Kev 2 ntawm 3: Muab Cov Hauv Paus Los Los Ntawm Coefficients
Kauj Ruam 1. Muab cov coefficients sib npaug
Coefficients yog cov lej uas nyob sab nraum lub hauv paus. Yog tias tsis muaj tus lej coefficient tau teev tseg, tom qab ntawd coefficient yog 1. Muab cov lej sib npaug. Nov yog koj ua nws li cas:
-
Piv txwv 1: 3√ (2) x (10) = 3√ (?)
3 x 1 = 3 po
-
Piv txwv 2: 4√ (3) x 3√ (6) = 12√ (?)
4x 3 = 12
Kauj Ruam 2. Muab cov zauv tso rau hauv paus
Thaum koj tau ua tiav qhov sib npaug, koj tuaj yeem muab tus lej hauv cov hauv paus hniav. Nov yog koj ua nws li cas:
- Piv txwv 1: 3√ (2) x (10) = 3√ (2 x 10) = 3√ (20)
- Piv txwv 2: 4√ (3) x 3√ (6) = 12√ (3 x 6) = 12√ (18)
Kauj Ruam 3. Ua kom yooj yim ntawm cov khoom
Tom ntej no, ua kom yooj yim cov lej hauv qab cov hauv paus hniav los ntawm kev nrhiav cov xwmfab zoo lossis ntau ntawm cov lej hauv qab cov hauv paus uas zoo sib xws. Thaum koj tau yooj yim cov ntsiab lus, tsuas yog muab lawv los ntawm cov coefficients. Nov yog koj ua nws li cas:
- 3√ (20) = 3√ (4 x 5) = 3√ ([2 x 2] x 5) = (3 x 2) √ (5) = 6√ (5)
- 12√ (18) = 12√ (9 x 2) = 12√ (3 x 3 x 2) = (12 x 3) √ (2) = 36√ (2)
Txoj Kev 3 ntawm 3: Muab Cov Hauv Paus Los Ntawm Qhov Ntsuas Sib Txawv
Kauj Ruam 1. Nrhiav LCM (tsawg tshaj plaws ntau yam) ntawm qhov ntsuas
Txhawm rau nrhiav LCM ntawm qhov ntsuas, nrhiav tus lej tsawg tshaj plaws uas tau faib los ntawm ob qho ntsuas. Nrhiav LCM ntawm qhov ntsuas ntawm qhov sib npaug hauv qab no:3(5) xwm 2√(2) = ?
Qhov ntsuas yog 3 thiab 2. 6 yog LCM ntawm ob tus lej no vim tias 6 yog tus lej tsawg tshaj plaws uas faib tau los ntawm ob qho 3 thiab 2. 6/3 = 2 thiab 6/2 = 3. Txhawm rau txhawm rau cov hauv paus hniav, ob qho ntsuas yuav tsum hloov mus rau 6
Kauj Ruam 2. Sau txhua nqe lus nrog LCM tshiab raws li nws qhov ntsuas
Nov yog qhov qhia hauv kab zauv nrog qhov ntsuas tshiab:
6(5) xwm 6√(2) = ?
Kauj Ruam 3. Nrhiav tus lej uas koj yuav tsum siv txhawm rau txhawm rau txhawm rau txhawm rau nrhiav nws qhov LCM
Rau kev qhia 3(5), koj yuav tsum muab tus lej ntsuas 3 los ntawm 2 kom tau 6. Rau qhov qhia tawm 2(2), koj yuav tsum muab tus lej ntsuas 2 los ntawm 3 kom tau 6.
Kauj Ruam 4. Ua tus lej no tus lej ntawm tus lej sab hauv hauv paus
Rau thawj qhov kev ua zauv, ua tus lej 2 raws li tus lej ntawm tus lej 5. Rau qhov kev ua zauv ob, ua tus lej 3 ua tus zauv ntawm tus lej 2. Nov yog qhov sib npaug:
- 2 6√(5) = 6√(5)2
- 3 6√(2) = 6√(2)3
Kauj Ruam 5. Muab cov zauv zauv hauv paus los ntawm tus zauv
Nov yog koj ua nws li cas:
- 6√(5)2 = 6(5 x 5) = np 6√25
- 6√(2)3 = 6(2 x 2 x 2) = 6√8
Kauj Ruam 6. Muab cov lej no tso rau hauv ib lub hauv paus
Muab tus lej tso rau hauv qab ib lub hauv paus thiab txuas lawv nrog cov lej sib npaug. Nov yog qhov tshwm sim: 6(8 x 25) Xauv
Kauj Ruam 7
6(8 x 25) = np 6(200). Nov yog lo lus teb kawg. Qee qhov xwm txheej, koj tuaj yeem ua kom yooj yim cov lus qhia no - piv txwv li, koj tuaj yeem ua qhov sib npaug no yooj yim yog tias koj pom tus lej uas tuaj yeem muab sib npaug ntawm nws tus kheej 6 zaug thiab yog qhov tseem ceeb ntawm 200. Tab sis qhov no, qhov kev nthuav qhia tsis tuaj yeem yooj yim. ib qho ntxiv
Lub tswv yim
- Yog tias "coefficient" raug cais los ntawm cov cim hauv paus los ntawm kev ntxiv lossis rho tawm kos npe, nws tsis yog qhov sib npaug - nws yog lub sijhawm cais thiab yuav tsum tau ua haujlwm cais los ntawm lub hauv paus. Yog tias lub hauv paus thiab lwm lub sijhawm nyob hauv tib lub ntsej muag - piv txwv li (2 + (hauv paus) 5), koj yuav tsum suav 2 thiab (hauv paus) 5 cais thaum ua haujlwm hauv cov khoom sib dhos, tab sis thaum ua haujlwm sab nraud ntawm cov zauv, koj yuav tsum suav (2 + (hauv paus) 5) ua ib chav tsev.
- Qhov "coefficient" yog tus lej, yog tias muaj, uas tau muab tso tam sim ua ntej lub hauv paus cag. Yog li piv txwv, hauv qhov kev qhia 2 (hauv paus) 5, 5 nyob hauv qab tus cim ntawm lub hauv paus thiab tus lej 2 nyob sab nraum lub hauv paus, uas yog qhov sib npaug. Thaum cov hauv paus hniav thiab cov coefficient tau muab tso ua ke, nws txhais tau tias zoo ib yam li muab cov hauv paus los ntawm qhov sib koom ua ke, lossis txuas ntxiv qhov piv txwv mus rau 2 * (hauv paus) 5.
- Lub hauv paus kos npe yog lwm txoj hauv kev los nthuav qhia qhov nthuav tawm ntawm ib feem. Hauv lwm lo lus, lub hauv paus cag ntawm ib tus lej sib npaug tus lej rau lub zog ntawm 1/2, lub hauv paus hauv paus ntawm ib tus lej sib npaug tus lej rau lub zog ntawm 1/3, thiab ntxiv rau.
