Txhawm rau ntxiv thiab rho tawm cov hauv paus cag, koj yuav tsum ua ke cov ntsiab lus hauv qhov kev ua zauv uas muaj tib lub hauv paus xwm txheej (radical). Qhov no txhais tau tias koj tuaj yeem ntxiv lossis rho tawm 2√3 thiab 4√3, tab sis tsis yog 2√3 thiab 2√5. Muaj ntau yam teeb meem uas tso cai rau koj yooj yim cov lej hauv cov hauv paus hauv paus yog li ntawd cov ntsiab lus tuaj yeem ua ke thiab cov hauv paus tuaj yeem muab ntxiv lossis rho tawm.
Kauj ruam
Ntu 1 ntawm 2: Nkag Siab Lub Hauv Paus
Kauj Ruam 1. Ua kom yooj yim tag nrho cov ntsiab lus hauv cov hauv paus plaub fab thaum twg los tau
Txhawm rau ua kom yooj yim cov ntsiab lus hauv cov hauv paus cag, sim ua qhov tseeb kom tsawg kawg ib lub sijhawm yog lub xwmfab zoo meej, xws li 25 (5 x 5) lossis 9 (3 x 3). Yog tias yog, coj lub hauv paus square zoo tshaj plaws thiab tso nws sab nraum lub hauv paus cag. Yog li, qhov tseem tshuav yog sab hauv lub hauv paus cag. Piv txwv li, peb cov teeb meem lub sijhawm no yog 6√50 - 2√8 + 5√12. Cov lej sab nraud ntawm lub hauv paus square yog hu ua "coefficients", thiab cov lej sab hauv cov hauv paus plaub yog cov radicands. Nov yog yuav ua li cas kom yooj yim rau txhua lub sijhawm:
- 6√50 = 6√ (25 x 2) = (6 x 5) √2 = 30√2. Ntawm no, koj ntsuas "50" rau "25 x 2" thiab tom qab ntawd hauv paus tus lej square zoo meej "25" txog "5" thiab muab tso rau sab nraum lub hauv paus cag, tso tus lej "2" sab hauv. Tom qab ntawd, suav cov lej sab nraum lub hauv paus square ntawm "5" los ntawm "6", kom tau "30" raws li qhov sib npaug tshiab
- 2√8 = 2√ (4 x 2) = (2 x 2) √2 = 4√2. Ntawm no, koj ntsuas "8" rau "4 x 2" thiab hauv paus tus lej zoo meej "4" txog "2" thiab muab tso rau sab nraum lub hauv paus plaub fab, tso tus lej "2" sab hauv. Tom qab ntawd, muab cov lej nyob sab nraum lub hauv paus cag, piv txwv li "2" los ntawm "2" kom tau "4" raws li qhov sib npaug tshiab.
- 5√12 = 5√ (4 x 3) = (5 x 2) √3 = 10√3. Ntawm no, koj ntsuas "12" rau hauv "4 x 3" thiab hauv paus "4" rau "2" thiab muab tso rau sab nraum lub hauv paus cag, tso tus lej "3" sab hauv. Tom qab ntawd, muab cov lej sab nraum lub hauv paus square ntawm "2" los ntawm "5", kom tau "10" raws li qhov sib npaug tshiab.
Kauj Ruam 2. Lub voj voos tag nrho cov ntsiab lus nrog tib lub radicand
Tom qab koj yooj yim radicand ntawm cov lus tau muab, koj qhov kev ua zauv zoo li qhov no 30√2 - 4√2 + 10√3. Txij li koj tsuas yog ntxiv lossis rho tawm ib yam li cov ntsiab lus, ncig cov ntsiab lus uas muaj tib lub hauv paus cag, xws li 30√2 thiab 4√2. Koj tuaj yeem xav txog nws tib yam li kev ntxiv thiab rho tawm cov zauv, uas tsuas tuaj yeem ua tiav yog tias cov lej yog tib yam.
Kauj Ruam 3. Rearrange cov kab lus ua ke hauv kab zauv
Yog tias koj qhov teeb meem sib npaug ntev txaus, thiab muaj ob peb khub ntawm radicands sib npaug, koj yuav tsum tau puag ncig thawj khub, sau kab thib ob, muab lub hnub qub tso rau hauv khub thib peb, thiab ntxiv rau. Rearrange cov kab zauv kom phim lawv cov khub kom cov lus nug tuaj yeem pom thiab ua tau yooj yim dua.
Kauj Ruam 4. Ntxiv lossis rho tawm cov coefficients ntawm cov ntsiab lus uas muaj radicand tib yam
Tam sim no, txhua yam koj yuav tsum ua yog ntxiv lossis rho tawm cov coefficients los ntawm cov ntsiab lus uas muaj tib lub radicand, tawm tag nrho cov ntsiab lus ntxiv uas yog ib feem ntawm qhov kev ua zauv. Tsis txhob muab cov radicands sib npaug. Koj yooj yim qhia tag nrho cov hom radicands hauv kab zauv. Cov pab pawg sib txawv yuav raug tso tseg raws li lawv nyob. Nov yog yam koj yuav tsum tau ua:
- 30√2 - 4√2 + 10√3 =
- (30 - 4)√2 + 10√3 =
- 26√2 + 10√3
Ntu 2 ntawm 2: Xyaum Ua Ntau Yam
Kauj Ruam 1. Ua Haujlwm Piv Txwv 1
Hauv qhov piv txwv no, koj ntxiv cov zauv hauv qab no: (45) + 4√5. Nov yog yuav ua li cas:
- Yooj yim (45). Ua ntej, muab nws tso rau hauv (9 x 5).
- Tom qab ntawd, koj tuaj yeem cag tus lej zoo meej "9" txog "3" thiab muab tso rau sab nraum lub hauv paus cag ua qhov sib koom ua ke. Yog li, (45) = 3√5.
- Tam sim no, tsuas yog ntxiv cov coefficients ntawm ob nqe lus nrog tib lub radicand kom tau txais cov lus teb 3√5 + 4√5 = 7√5
Kauj Ruam 2. Ua Haujlwm Piv Txwv 2
Qhov teeb meem piv txwv no yog: 6√ (40) - 3√ (10) + 5. Nov yog yuav daws nws li cas:
- Ua kom yooj yim 6√ (40). Ua ntej, qhov "40" kom tau "4 x 10". Yog li, koj qhov sib npaug ua 6√ (40) = 6√ (4 x 10).
- Tom qab ntawd, siv cov hauv paus plaub fab ntawm tus lej zoo meej "4" rau "2", tom qab ntawd muab nws sib npaug los ntawm qhov sib npaug uas twb muaj lawm. Tam sim no koj tau txais 6√ (4 x 10) = (6 x 2) √10.
- Muab ob tus coefficients kom tau 12-10.
- Tam sim no, koj qhov sib npaug dhau los ua 12-10 - 3√ (10) + 5. Txij li ob nqe lus muaj tib lub radicand, koj tuaj yeem rho thawj lub sijhawm los ntawm qhov thib ob, thiab tawm lub sijhawm thib peb raws li nws yog.
- Qhov tshwm sim yog (12-3) √10 + 5, uas tuaj yeem ua kom yooj yim rau 9√10 + 5.
Kauj Ruam 3. Ua Haujlwm Piv Txwv 3
Qhov teeb meem piv txwv no yog raws li hauv qab no: 9√5 -2√3 - 4√5. Ntawm no, tsis muaj cov hauv paus hauv paus muaj qhov zoo sib xws tus lej tooj. Yog li, qhov sib npaug tsis tuaj yeem yooj yim. Cov ntsiab lus thawj thiab thib peb muaj tib lub radicand yog li lawv tuaj yeem sib xyaw ua ke, thiab cov radicand tau tso tseg ib yam. Tus so, tsis muaj ib yam radican ntxiv lawm. Yog li, qhov teeb meem tuaj yeem yooj yim rau 5-5 - 2-3.
Kauj Ruam 4. Ua Haujlwm Piv Txwv 4
Qhov teeb meem yog: 9 + 4 - 3√2. Nov yog yuav ua li cas:
- Txij li 9 sib npaug rau (3 x 3), koj tuaj yeem yooj yim 9 txog 3.
- Txij li 4 sib npaug rau (2 x 2), koj tuaj yeem yooj yim 4 rau 2.
- Tam sim no, koj tsuas yog xav tau ntxiv 3 + 2 kom tau 5.
- Txij li 5 thiab 3√2 tsis yog tib lub sijhawm, tsis muaj dab tsi ntxiv tuaj yeem ua tiav. Cov lus teb zaum kawg yog 5 - 3√2.
Kauj Ruam 5. Ua Haujlwm Piv Txwv 5
Sim ntxiv thiab rho tawm cov hauv paus plaub fab uas yog ib feem ntawm cov feem. Zoo li cov lej ib txwm, koj tsuas tuaj yeem ntxiv lossis rho tawm cov feem uas muaj cov lej sib npaug. Hais qhov teeb meem yog: (√2)/4 + (√2)/2. Nov yog yuav daws nws li cas:
- Hloov cov ntsiab lus no kom lawv muaj cov lej sib npaug. Qhov tsawg tshaj plaws sib txawv (LCM), uas yog tus lej tsawg tshaj plaws uas tau faib los ntawm ob tus lej sib xws, ntawm cov lej "4" thiab "2," yog "4."
- Yog li hloov lub sijhawm thib ob, (√2)/2 kom tus lej yog 4. Koj tuaj yeem muab tus zauv sib faib thiab faib ua feem ntawm 2/2. (√2)/2 x 2/2 = (2√2)/4.
- Ntxiv ob tus lej ua ke yog tias cov lej yog tib yam. Ua haujlwm zoo li ntxiv cov lej ib txwm. (√2)/4 + (2√2)/4 = 3√2)/4.
Lub tswv yim
Txhua lub hauv paus cag uas muaj qhov xwm txheej zoo tshaj yuav tsum ua kom yooj yim ua ntej pib txheeb xyuas thiab sib koom ua ke radicans.
Ceeb toom
- Tsis txhob muab cov hauv paus sib npaug sib npaug.
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Tsis txhob muab cov lej sib npaug nrog cov hauv paus cag. Ntawd yog, 3 + (2x)1/2 tsis tau yooj yim.
Nco tseg: kab lus "(2x) rau lub zog ib nrab" = (2 x)1/2 tsuas yog lwm txoj kev hais "hauv paus (2x)".
