סדרה 4 — חזקות ושורשים

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שלוש עשרה שאלות בפורמט המבחן. כדאי להפעיל שעון: עשר דקות, בלי מחשבון. בכל תרגיל — קודם מסמנים מה מחשבים ראשון, ורק אחר כך מחשבים.

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כמה זה 262^{6}?

Exercises

Exercise 1

כמה זה 262^{6}?

  1. A6464
  2. B3636
  3. C1212
  4. D3232
Show the answer and the solution

Answer: A 6464

Worked solution:

2×2×2×2×2×2=642 \times 2 \times 2 \times 2 \times 2 \times 2 = 64

התשובה היא 6464. 12=2×612 = 2 \times 6, ו-36=6236 = 6^{2} — הבסיס והמעריך התחלפו.

Check the answer on elev Bar-Ilan — Exercise 1

Exercise 2

כמה זה 144\sqrt{144}?

  1. A2424
  2. B1212
  3. C1414
  4. D7272
Show the answer and the solution

Answer: B 1212

Worked solution:

12×12=14412 \times 12 = 144

התשובה היא 1212. 72=144:272 = 144 : 2 — שורש אינו חצי.

Check the answer on elev Bar-Ilan — Exercise 2

Exercise 3

כמה זה 535^{3}?

  1. A243243
  2. B2525
  3. C1515
  4. D125125
Show the answer and the solution

Answer: D 125125

Worked solution:

5×5×5=1255 \times 5 \times 5 = 125

התשובה היא 125125. 243=35243 = 3^{5}.

Check the answer on elev Bar-Ilan — Exercise 3

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Exercise 4

כמה זה 343^{4}?

Show the answer and the solution

Answer: 81

Worked solution:

3×3=9  9×9=81\begin{aligned}3 \times 3 &= 9 \\ \; 9 \times 9 &= 81\end{aligned}

8181. קיצור: 34=(32)2=923^{4} = (3^{2})^{2} = 9^{2}.

Check the answer on elev Bar-Ilan — Exercise 4

Exercise 5

בין אילו שני מספרים שלמים נמצא 90\sqrt{90}?

  1. A4545 ל-4646
  2. B88 ל-99
  3. C1010 ל-1111
  4. D99 ל-1010
Show the answer and the solution

Answer: D 99 ל-1010

Worked solution:

92=81<90<100=102\begin{aligned}9^{2} &= 81 < 90 < 100 \\ &= 10^{2}\end{aligned}

התשובה היא 99 ל-1010.

Check the answer on elev Bar-Ilan — Exercise 5

Exercise 6

16+9=4+3\sqrt{16 + 9} = 4 + 3

Show the answer and the solution

Answer: False

Worked solution:

16+9=25=5\begin{aligned}\sqrt{16 + 9} &= \sqrt{25} \\ &= 5\end{aligned}
4+3=74 + 3 = 7

לא נכון. השורש חל על התוצאה של הסכום: קודם מחברים, אחר כך מוציאים שורש.

Check the answer on elev Bar-Ilan — Exercise 6

Exercise 7

210>1032^{10} > 10^{3}

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Answer: True

Worked solution:

210=10242^{10} = 1024
103=100010^{3} = 1000

נכון, בקצת: 1024>10001024 > 1000.

Check the answer on elev Bar-Ilan — Exercise 7

Exercise 8

כמה זה (2×5)3(2 \times 5)^{3}?

  1. A250250
  2. B10001000
  3. C100100
  4. D3030
Show the answer and the solution

Answer: B 10001000

Worked solution:

2×5=102 \times 5 = 10
103=100010^{3} = 1000

התשובה היא 10001000. 250=2×53250 = 2 \times 5^{3} — החזקה חלה על כל הסוגריים.

Check the answer on elev Bar-Ilan — Exercise 8

Exercise 9

סידור מהקטן לגדול.

  • 900\sqrt{900}
  • 252^{5}
  • 333^{3}
  • 626^{2}
Show the answer and the solution

Answer: 333^{3} · 900\sqrt{900} · 252^{5} · 626^{2}

Worked solution:

27<30<32<3627 < 30 < 32 < 36

33=273^{3} = 27, 900=30\sqrt{900} = 30, 25=322^{5} = 32, 62=366^{2} = 36.

Check the answer on elev Bar-Ilan — Exercise 9

Exercise 10

לאיזה מספר שלם הכי קרוב 50\sqrt{50}?

  1. A2525
  2. B77
  3. C55
  4. D88
Show the answer and the solution

Answer: B 77

Worked solution:

72=49  82=64\begin{aligned}7^{2} &= 49 \\ \; 8^{2} &= 64\end{aligned}
50−49=1<64−50=14\begin{aligned}50 - 49 &= 1 < 64 - 50 \\ &= 14\end{aligned}

התשובה היא 77: 50≈7.07\sqrt{50} \approx 7.07. 25=50:225 = 50 : 2.

Check the answer on elev Bar-Ilan — Exercise 10

Exercise 11

התאמה בין ביטויים שווים.

  • 262^{6}
  • 343^{4}
  • 10210^{2}
  • 525^{2}
  • 10,000\sqrt{10{,}000}
  • 625\sqrt{625}
  • 828^{2}
  • 929^{2}
Show the answer and the solution

Answer: 262^{6} — 828^{2} · 343^{4} — 929^{2} · 10210^{2} — 10,000\sqrt{10{,}000} · 525^{2} — 625\sqrt{625}

Worked solution:

26=64=82\begin{aligned}2^{6} &= 64 \\ &= 8^{2}\end{aligned}
34=81=92\begin{aligned}3^{4} &= 81 \\ &= 9^{2}\end{aligned}
10,000=100\sqrt{10{,}000} = 100
625=25\sqrt{625} = 25

כל זוג שווה בערכו, גם כשהוא כתוב אחרת.

Check the answer on elev Bar-Ilan — Exercise 11

Exercise 12

כמה זה 24+32\sqrt{2^{4} + 3^{2}}?

  1. A13\sqrt{13}
  2. B55
  3. C2525
  4. D77
Show the answer and the solution

Answer: B 55

Worked solution:

24=16  32=9\begin{aligned}2^{4} &= 16 \\ \; 3^{2} &= 9\end{aligned}
16+9=25=5\begin{aligned}\sqrt{16 + 9} &= \sqrt{25} \\ &= 5\end{aligned}

התשובה היא 55. 7=4+37 = 4 + 3 — שורש לכל איבר בנפרד, וזו טעות.

Check the answer on elev Bar-Ilan — Exercise 12

Exercise 13

מה ספרת האחדות של 3203^{20}?

  1. A77
  2. B99
  3. C33
  4. D11
Show the answer and the solution

Answer: D 11

Worked solution:

31→3,  32→9,  33→7,  34→13^{1} \to 3,\; 3^{2} \to 9,\; 3^{3} \to 7,\; 3^{4} \to 1

מחזור של 44

20=4×520 = 4 \times 5

3203^{20} בסוף מחזור

התשובה היא 11. ספרות האחדות של חזקות 33 חוזרות כל 44: 3,9,7,13, 9, 7, 1.

Check the answer on elev Bar-Ilan — Exercise 13

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This lesson is part of the subscription. A full chapter for free: Logical reasoning