Yuav Ua Li Cas Ntxiv thiab Rho Tawm Cov Hauv Paus Square: 9 Kauj Ruam

Cov txheej txheem:

Yuav Ua Li Cas Ntxiv thiab Rho Tawm Cov Hauv Paus Square: 9 Kauj Ruam
Yuav Ua Li Cas Ntxiv thiab Rho Tawm Cov Hauv Paus Square: 9 Kauj Ruam

Video: Yuav Ua Li Cas Ntxiv thiab Rho Tawm Cov Hauv Paus Square: 9 Kauj Ruam

Video: Yuav Ua Li Cas Ntxiv thiab Rho Tawm Cov Hauv Paus Square: 9 Kauj Ruam
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Txhawm rau ntxiv lossis rho tawm cov hauv paus cag, koj yuav tsum tau ua ke cov hauv paus hniav uas muaj tib lub sij hawm zoo li lub radial. Qhov no txhais tau tias koj tuaj yeem ntxiv thiab rho tawm 2√3 thiab 4√3, tab sis tsis yog 2√3 thiab 2√5. Muaj ntau qhov xwm txheej uas nws muaj peev xwm ua kom yooj yim tus lej hauv cov radical kom lawv tuaj yeem ua ke ua cov ntsiab lus thiab tom qab ntawd ntxiv thiab tshem tawm cov hauv paus cag.

cov kauj ruam

Ntu 1 ntawm 2: Kev Paub Txog Lub Hauv Paus

Ntxiv thiab rho tawm Square Roots Kauj Ruam 1
Ntxiv thiab rho tawm Square Roots Kauj Ruam 1

Kauj Ruam 1. Ua kom yooj yim txhua lub sijhawm hauv lub qia yog ua tau

Txhawm rau ua qhov no, sim ua cov ntsiab lus kom pom tsawg kawg ib lo lus uas yog lub xwmfab zoo tshaj, xws li 25 (5 x 5) lossis 9 (3 x 3). Tom qab ntawd koj tuaj yeem siv lub hauv paus cag ntawm lub xwmfab zoo tshaj plaws thiab sau nws sab nrauv, tawm hauv qhov seem uas seem hauv nws. Hauv qhov piv txwv no, peb yuav siv cov teeb meem hauv qab no: 6√50 - 2√8 + 5√12. Cov lej sab nraum cov radical yog cov coefficients thiab cov lej sab hauv yog radicands. Saib yuav ua li cas thiaj yooj yim rau txhua nqe lus:

  • 6√50 = 6√ (25 x 2) = (6 x 5) √2 = 30√2. Hauv qhov piv txwv no, koj ntsuas "50" rau "25 x 2" thiab coj "5" los ntawm lub hauv paus zoo, "25", thiab tso nws tawm sab nrauv, nrog "2" tshuav nyob hauv nws. Tom qab ntawd koj muab "5" los ntawm "6", tus lej sab nraud tawm tsam, kom tau "30" raws li qhov sib npaug tshiab.
  • 2√8 = 2√ (4 x 2) = (2 x 2) √2 = 4√2. Hauv qhov piv txwv no, koj ntsuas "8" rau "4 x 2" thiab coj "2" los ntawm lub hauv paus zoo, "4", thiab tso nws tawm sab nrauv, nrog "2" sab hauv nws. Tom qab ntawd koj muab "2" los ntawm "2", tus lej sab nraud tawm tsam, kom tau "4" raws li qhov sib npaug tshiab.
  • 5√12 = 5√ (4 x 3) = (5 x 2) √3 = 10√3. Hauv qhov piv txwv no, koj ntsuas "12" rau hauv "4 x 3" thiab coj "2" los ntawm lub hauv paus zoo, "4", thiab tso nws tawm sab nrauv, nrog qhov "3" hauv nws. Tom qab ntawd koj muab "2" los ntawm "5", tus lej sab nraud tawm tsam, kom tau "10" raws li qhov sib npaug tshiab.
Ntxiv thiab rho tawm Square Roots Kauj Ruam 2
Ntxiv thiab rho tawm Square Roots Kauj Ruam 2

Kauj Ruam 2. Qhib ib nqe lus twg nrog cov radicands sib npaug

Tom qab ua kom yooj yim cov ntsiab lus 'radicands, qhov sib npaug yuav zoo li no: 30√2 - 4√2 + 10√3. Txij li nws tsuas yog ua tau ntxiv lossis rho tawm tib cov ntsiab lus, kos cov ntsiab lus uas muaj tib yam nkaus. Hauv qhov piv txwv siv, cov ntsiab lus yog 30√2 thiab 4√2. Xav txog cov txheej txheem no zoo ib yam li kev ntxiv lossis rho tawm feem feem, qhov twg koj tsuas tuaj yeem ua qhov no nrog cov ntsiab lus ntawm tib tus lej.

Ntxiv thiab rho tawm Square Roots Kauj Ruam 3
Ntxiv thiab rho tawm Square Roots Kauj Ruam 3

Kauj Ruam 3. Yog tias koj tab tom ua haujlwm nrog kab zauv qhov ntev uas muaj ntau khub nrog cov radicands sib npaug, koj tuaj yeem hla thawj tus khub, kos kab thib ob, thiab muab lub hnub qub tso rau hauv peb, thiab ntxiv rau

Teem cov ntsiab lus los ua kom pom kev yooj yim dua.

Ntxiv thiab rho tawm Square Roots Kauj Ruam 4
Ntxiv thiab rho tawm Square Roots Kauj Ruam 4

Kauj Ruam 4. Ntxiv lossis rho tawm cov coefficients ntawm cov ntsiab lus nrog radicands sib npaug

Tam sim no txhua yam koj yuav tsum tau ua yog ntxiv lossis rho tawm cov coefficients los ntawm cov ntsiab lus nrog radicands sib npaug thiab tawm ib nqe lus ntxiv uas yog ib feem ntawm qhov sib npaug. Tsis txhob sib xyaw radicands. Lub tswv yim yog txhawm rau txheeb xyuas seb muaj pes tsawg hom radicals muaj nyob hauv tag nrho. Cov ntsiab lus sib txawv yuav nyob zoo ib yam. Ua cov hauv qab no:

  • 30√2 - 4√2 + 10√3 =
  • (30 - 4)√2 + 10√3 =
  • 26√2 + 10√3

Ntu 2 ntawm 2: Xyaum ua ntxiv

Ntxiv thiab rho tawm Square Roots Kauj Ruam 5
Ntxiv thiab rho tawm Square Roots Kauj Ruam 5

Kauj Ruam 1. Piv txwv 1

Hauv qhov piv txwv no, ntxiv cov hauv paus hauv qab no: √ (45) + 4√5. Ua cov hauv qab no:

  • Yooj Yim √ (45). Ua ntej tshaj, kom tau txais √ (9 x 5).
  • Tom qab ntawd coj tus "3" los ntawm cov hauv paus square zoo tshaj, "9", thiab ua kom nws qhov sib npaug ntawm cov radical. Yog li √ (45) = 3√5.
  • Tam sim no, tsuas yog ntxiv cov coefficients ntawm ob nqe lus nrog radicands sib npaug kom tau txais cov lus teb. 3√5 + 4√5 = 7√5
Ntxiv thiab rho tawm Square Roots Kauj Ruam 6
Ntxiv thiab rho tawm Square Roots Kauj Ruam 6

Kauj Ruam 2. Piv txwv 2

Hauv qhov piv txwv no, teeb meem muaj raws li hauv qab no: 6√ (40) - 3√ (10) + √5. Ua cov hauv qab no:

  • Ua kom yooj yim 6√ (40). Ua ntej, ntsuas "40" kom tau "4 x 10", ua rau 6√ (40) = 6√ (4 x 10).
  • Tom qab ntawd coj tus "2" los ntawm cov hauv paus square zoo tshaj, "3", thiab muab nws suav nrog qhov sib piv tam sim no. Tam sim no, koj muaj 6√ (4 x 10) = (6 x 2) √10.
  • Muab ob tus coefficients kom tau 12-10.
  • Tam sim no qhov teeb meem yog qhov no: 12√10 - 3√ (10) + √5. Txij li thawj ob nqe lus muaj tib lub radicands, koj tuaj yeem rho lub sijhawm thib ob los ntawm thawj zaug thiab tawm qhov thib peb raws li yog.
  • Tam sim no qhov teeb meem tau hloov pauv mus rau (12-3) √10 + √5, uas tuaj yeem ua kom yooj yim rau 9√10 + √5.
Ntxiv thiab rho tawm Square Roots Kauj Ruam 7
Ntxiv thiab rho tawm Square Roots Kauj Ruam 7

Kauj Ruam 3. Piv txwv 3

Hauv qhov piv txwv no, qhov teeb meem yog raws li hauv qab no: 9√5 -2√3 - 4-5√. Ntawm no, tsis muaj ib qho ntawm cov radicals muaj cov yam ntxwv uas zoo sib xws, yog li kev yooj yim tsis tuaj yeem ua tau. Thawj thiab thib peb cov ntsiab lus yog sib npaug radicals, yog li lawv cov coefficients tuaj yeem ua ke (9-4). Lub radicand tsis hloov pauv. Cov ntsiab lus tseem tshuav tsis sib npaug, yog li cov teeb meem tuaj yeem yooj yim rau 5-5 - 2-3.

Ntxiv thiab rho tawm Square Roots Kauj Ruam 8
Ntxiv thiab rho tawm Square Roots Kauj Ruam 8

Kauj Ruam 4. Piv txwv 4

Cia peb hais qhov teeb meem yog qhov no: √9 + √4 - 3√2. Ua cov hauv qab no:

  • Txij li √9 zoo ib yam li √ (3 x 3), koj tuaj yeem yooj yim √9 txog 3.
  • Txij li √4 zoo ib yam li √ (2 x 2), koj tuaj yeem yooj yim √4 rau 2.
  • Tam sim no koj tuaj yeem ntxiv 3 + 2 kom tau 5.
  • Txij li 5 thiab 3√2 tsis yog nqe lus sib luag, tsis muaj dab tsi ntxiv los ua. Cov lus teb zaum kawg yog 5 - 3√2.
Ntxiv thiab rho tawm Square Roots Kauj Ruam 9
Ntxiv thiab rho tawm Square Roots Kauj Ruam 9

Kauj Ruam 5. Piv txwv 5

Cia peb sim ntxiv thiab rho tawm cov lej keeb kwm uas yog ib feem ntawm ib feem. Tam sim no, ib yam li cov feem ib txwm muaj, koj tsuas tuaj yeem ntxiv lossis rho tawm cov feem uas muaj cov lej lossis cov lej sib npaug. Cia peb hais qhov teeb meem yog raws li hauv qab no: (√2)/4 + (√2)/2. Ua cov hauv qab no:

  • Ua kom cov ntsiab lus muaj cov lej sib npaug. Qhov sib faib qis tshaj, lossis cov lej sib faib los ntawm ob qho lej, "4" thiab "2," yog "4".
  • Yog li txhawm rau ua lub sijhawm thib ob, (√2)/2, muaj tus lej 4, koj yuav tsum tau muab nws tus lej thiab tus lej faib ua 2/2. (√2)/2 x 2/2 = (2√2)/4.
  • Ntxiv cov zauv lej thiab khaws cov lej sib npaug ib yam. Ua tib yam li koj xav tau thaum ntxiv cov lej faib. (√2)/4 + (2√2)/4 = 3√2)/4.

Lub tswv yim

Ib txwm ua kom yooj yim txhua qhov radicals uas muaj cov hauv paus zoo hauv paus ua ntej kom pib txheeb xyuas thiab sib npaug radicands sib npaug.

Cov ntawv ceeb toom

  • Tsis txhob sib xyaw cov radicals sib txawv.
  • Tsis txhob muab cov lej sib xyaw nrog cov radical kom: 3 + (2x)1/2 tsis tuaj yeem ua kom yooj yim.

    Nco tseg: hais "ib nrab lub zog ntawm (2x)" = (2 x)1/2 yog lwm txoj kev hais "square hauv paus ntawm (2x)".

Pom zoo: