Rov qab mus rau tsev kawm ntawv. hauv paus tas li ntawd

Niaj hnub no niaj hnub hluav taws xob computers xam cov square hauv paus ntawm tus xov tooj tsis yog ib tug yooj yim ua hauj lwm. Piv txwv li, √2704 = 52, qhov no yog koj xam tej tswvyim. Qhov zoo ces, tus tswvyim yog tsis tsuas yog nyob rau lub qhov rais, tab sis kuj nyob rau hauv lub dog dig, txawm lub feem ntau unpretentious, xov tooj. Muaj tseeb yog tias mam li nco dheev (ib tug tsawg qhov muaj tseeb, le caag ntawm uas, incidentally, muaj xws li qhov sib ntxiv ntawm cov hauv paus hniav), koj yuav nrhiav tau koj tus kheej tsis muaj nyiaj, ces, alas, muaj tso siab rau lawv lub hlwb.

Kev kawm rau cov siab yog tsis muab tso rau. Tshwj xeeb tshaj yog rau cov neeg uas tsis yog li ntawd feem ntau ua hauj lwm nrog cov zauv, thiab txawm ntau li ntawd nrog rau keeb kwm. Ntxiv thiab rho tawm yog cov hauv paus hniav - ib tug zoo workout rau lub siab dhuav. Thiab kuv mam li qhia koj kauj ruam yog kauj ruam ntxiv ntawm cov hauv paus hniav. Qhia Piv txwv tej zaum yuav raws li nram no.

Cov kab zauv uas yuav tsum tau yooj yim zog:

√2 + 3√48-4 × √27 + √128

Qhov no yog ib qho irrational qhia. Nyob rau hauv thiaj li yuav piv tau nws yog tsim nyog los nqa tag nrho cov radicands cov kev daim ntawv. Peb tsis ruam yog kauj ruam:

Tus ntawv zauv no yuav tsis tau yooj yim zog. Peb tig mus rau lub thib ob lub sij hawm.

3√48 decompose nyob rau hauv multipliers 48: 48 = 2 × 24 los yog 48 × 16 = 3. Lub square hauv paus ntawm 24 tsis yog ib qho integer, i.e. ib tug fractional seem. Txij li thaum peb yuav tsum tau lub caij nyoog muaj nuj nqis, approximate cov hauv paus hniav yog tsis haum. Lub square hauv paus ntawm 16 yog plaub, kom nws tawm los ntawm nyob rau hauv lub hauv paus kos npe rau. Peb tau 4 × 3 × √3 = 12 × √3

Cov nram qab no daim ntawv qhia los ntawm peb yog tsis zoo, piv txwv li, yog sau ntawv nrog ib tug rho tawm -4 × √ (27.) Kis 27 multipliers. Peb tau 27 × 3 = 9. Peb tsis txhob siv fractional multipliers vim hais tias ntawm lub fractions los mus laij lub square hauv paus ntawm lub complex. 9 coj tawm los ntawm nyob rau hauv lub phaj, i.e. Peb xam cov square hauv paus. Peb muab tau cov nram qab no qhia: -4 × 3 × √3 = -12 × √3

Tom ntej no lub sij hawm √128 xam qhov uas yuav tsum tau noj tawm los ntawm nyob rau hauv lub hauv paus. 128 = 64 × 2, nyob qhov twg √64 = 8. Yog hais tias koj muaj peev xwm xav txog tej yam nws yuav ua tau yooj yim dua no qhia raws li: √128 = √ (8 ^ 2 × 2)

Peb sau dua tshiab cov kev qhia yooj yim zog cov nqe lus:

√2 + 12 × √3-12 × √3 + 8 × √2

Tam sim no peb ntxiv li tus naj npawb ntawm tib radicals. Koj muaj peev xwm tsis ntxiv los sis rho qhia sib txawv ntawm cov radicals. hauv paus ntxiv yuav tsum tau ua raws li txoj cai no.

Peb tau txais hauv qab no cov lus teb:

√2 + 12√3-12√3 + 8√2 = 9√2

√2 = 1 × √2 - cia siab hais tias nyob rau hauv algebra txiav txim siab los tso tawm tej ntsiab yuav tsis muaj xov xwm rau koj.

Zaj lus yuav sawv cev tsis tau tsuas yog los ntawm cov square hauv paus, tab sis kuj nrog ib tug nyhav hauv paus los yog n-hydrochloric twg.

Ntxiv thiab rho tawm cov hauv paus hniav nrog txawv exponents, tab sis, nrog sib npaug radicand, yog raws li nram no:

Yog hais tias peb muaj ib qho kev qhia zoo li √a + ∛b + ∜b, peb yuav piv no qhia raws li nram no:

∛b + ∜b = 12 × √b4 + 12 × √b3

12√b4 + 12 × √b3 = 12 × √b4 + B3

Peb coj ob tug neeg mus rau ib tug ntau qhia ntawm lub hauv paus. Ntawm no yog peb tau siv cov hauv paus hniav ntawm cov cuab yeej, uas nyeem hais tias raws li nram no: yog hais tias lub xov tooj ntawm degrees ntawm radical qhia thiab tus naj npawb ntawm cov hauv paus hniav index khoo los ntawm tib lub xov tooj, nws cov xam tseem unchanged.

Nco ntsoov: lub exponents tsuas ntxiv txog thaum khoo.

Xav txog ib tug piv txwv uas tam sim no nyob rau hauv cov nqe lus ntawm lub feem.

5√8-4 × √ (1/4) + √72-4 × √2

Peb yuav txiav txim siab nyob rau hauv cov kauj ruam:

5√8 = 5 * 2√2 - peb ua kom tawm ntawm lub hauv paus ntawm lub retrievable.

- 4√ (1/4) = - 4 √1 / (√4) = - 4 * 1/2 = - 2

Yog hais tias lub hauv paus ntawm lub cev yog sawv cev los ntawm ib feem, lub feem tsis yog ib feem ntawm qhov kev hloov no, yog hais tias tus square hauv paus ntawm qhov tawn thiab cov divisor. Raws li ib tug tshwm sim, peb twb tau txais cov koob pheej ntawm lawv piav saum toj no.

√72-4√2 = √ (2 × 36) - 4√2 = 2√2

10√2 + 2√2-2 = 12√2-2

Yog li ntawd yuav tau txais ib lo lus teb.

Qhov loj tshaj plaws kom koj nco ntsoov hais tias cov zauv negative tsis tau ntiab cov hauv paus hniav nrog ib tug txawm exponent. Yog hais tias txawm degree radicand yog tsis zoo, ces tus qhia yog unsolvable.

Tsis tas li ntawd ntawm cov keeb kwm yog tau tsuas yog thaum lub coincidence ntawm kab zauv nyob rau hauv lub radicals vim hais tias lawv zoo sib xws cov lus. Tib yam siv rau lub sib txawv.

Tsis tas li ntawd ntawm numeric cov hauv paus hniav nrog txawv exponents ua los ntawm nqa rau tag nrho cov raws li ntawm lub hauv paus ntawm ob nqe lus. Qhov no txoj cai muaj cov nyhuv tib yam li ib tug yuav txo tau mus rau ib tug ntau denominator thaum muab los yog subtracting fractions.

Yog hais tias lub radicand muaj ib tug xov tooj tsa mus rau lub hwj chim ntawm no qhia yuav yooj yim zog los ntawm piv txwv tias yog hais tias lub hauv paus ntawm lub Performance index thiab raws li muaj ib qho denominator.