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Find the prime factors of 244036 and 103823. Hence, evaluate sqrt(244036)/cbrt(103823).

Mathematics

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2 parts
a

22×132×1922^2 \times 13^2 \times 19^2

47347^3

b

49447\frac{494}{47}

Step-by-step solution

8 steps

Huu hapa ni utatuzi wa swali lako:

Part a· 5 steps

Tafuta vigawo vikuu vya 244036 na 103823

Kwa 244036:

  1. Anza kugawanya kwa nambari kuu ndogo zaidi.

    244036÷2=122018244036 \div 2 = 122018 122018÷2=61009122018 \div 2 = 61009
  2. Endelea na nambari kuu zinazofuata.

    61009 haigawanyiki kwa 3, 5, 7, 11. Jaribu 13.

    61009÷13=469361009 \div 13 = 4693 4693÷13=3614693 \div 13 = 361
  3. Tambua nambari kuu iliyobaki.

    361 ni mraba wa 19.

    361÷19=19361 \div 19 = 19 19÷19=119 \div 19 = 1

    Hivyo, vigawo vikuu vya 244036 ni 2×2×13×13×19×192 \times 2 \times 13 \times 13 \times 19 \times 19.
    Katika fomu ya vipeo: 244036=22×132×192244036 = 2^2 \times 13^2 \times 19^2.

    Kwa 103823:

  4. Anza kugawanya kwa nambari kuu.

    103823 haigawanyiki kwa 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43. Jaribu 47.

    103823÷47=2209103823 \div 47 = 2209
  5. Endelea kugawanya.

    2209 ni mraba wa 47.

    2209÷47=472209 \div 47 = 47 47÷47=147 \div 47 = 1

    Hivyo, vigawo vikuu vya 103823 ni 47×47×4747 \times 47 \times 47.
    Katika fomu ya vipeo: 103823=473103823 = 47^3.

    Vigawo vikuu ni:
    244036=22×132×192244036 = \boxed{2^2 \times 13^2 \times 19^2}
    103823=473103823 = \boxed{47^3}

Part b

49447\frac{494}{47}

Kwa hivyo, tathmini 2440361038233\frac{\sqrt{244036}}{\sqrt[3]{103823}}

  1. Tafuta mzizi wa pili wa 244036.

    Kutoka sehemu (a), 244036=22×132×192244036 = 2^2 \times 13^2 \times 19^2.

    244036=22×132×192\sqrt{244036} = \sqrt{2^2 \times 13^2 \times 19^2} 244036=2×13×19\sqrt{244036} = 2 \times 13 \times 19 244036=26×19\sqrt{244036} = 26 \times 19 244036=494\sqrt{244036} = 494
  2. Tafuta mzizi wa tatu wa 103823.

    Kutoka sehemu (a), 103823=473103823 = 47^3.

    1038233=4733\sqrt[3]{103823} = \sqrt[3]{47^3} 1038233=47\sqrt[3]{103823} = 47
  3. Gawanya matokeo.

    2440361038233=49447\frac{\sqrt{244036}}{\sqrt[3]{103823}} = \frac{494}{47} 49447=10.510638...\frac{494}{47} = 10.510638...

    Kama sehemu, jibu ni 49447\frac{494}{47}.

    Thamani ya usemi ni 49447\boxed{\frac{494}{47}}.

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