We read your photo as:

List all the prime numbers between 100 to 120 and work out the product of the largest and the smallest prime numbers. Classify 1, 2 and sqrt(5) as rational or irrational numbers.

Mathematics

ScanSolve AI Answer

Answers

3 parts
6
11413
8
0.2
9
4.1779

Step-by-step solution

16 steps

Part 6· 3 steps

List all the prime numbers between 100 to 120 and work out the product of the largest and the smallest prime numbers.

  1. Identify prime numbers between 100 and 120.

    A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
    The prime numbers between 100 and 120 are:

    101,103,107,109,113101, 103, 107, 109, 113
  2. Identify the largest and smallest prime numbers from the list.

    Smallest prime number = 101
    Largest prime number = 113

  3. Calculate the product of the largest and smallest prime numbers.

    Product = 101×113101 \times 113

    101×113=11413101 \times 113 = 11413

    The product of the largest and smallest prime numbers is 11413\boxed{11413}.

Part 7· 4 steps

The shorter sides of a right angled triangle are 1 m and 2 m respectively. Its longest side is 5\sqrt{5} m. Classify 1, 2 and 5\sqrt{5} as rational or irrational numbers.

  1. Define rational and irrational numbers.

    A rational number can be expressed as a fraction pq\frac{p}{q} where pp and qq are integers and q≠0q \neq 0.
    An irrational number cannot be expressed as a simple fraction; its decimal representation is non-terminating and non-repeating.

  2. Classify 1.

    1 can be written as 11\frac{1}{1}. Therefore, 1 is a rational number.

  3. Classify 2.

    2 can be written as 21\frac{2}{1}. Therefore, 2 is a rational number.

  4. Classify 5\sqrt{5}.

    Since 5 is not a perfect square, 5\sqrt{5} cannot be expressed as a simple fraction. Its decimal representation is non-terminating and non-repeating (2.23606...). Therefore, 5\sqrt{5} is an irrational number.

Part 80.2

The Nairobi - Mombasa commuter train takes 5 hours to travel from Nairobi to Mombasa in the afternoon. What fraction of the journey does it cover in 1 hour using reciprocal tables.

  1. Determine the fraction of the journey covered in 1 hour.

    If the total journey takes 5 hours, then in 1 hour, the train covers 15\frac{1}{5} of the journey.

  2. Use reciprocal tables to find the value of 15\frac{1}{5}.

    Looking up the reciprocal of 5 in a reciprocal table gives:

    15=0.2\frac{1}{5} = 0.2

    The fraction of the journey covered in 1 hour is 0.2\boxed{0.2}.

Part 94.1779

Use mathematical tables to evaluate: 40.981+19.81\frac{4}{0.981} + \frac{1}{9.81}

  1. Rewrite the expression using reciprocals.

    40.981+19.81=4×10.981+19.81\frac{4}{0.981} + \frac{1}{9.81} = 4 \times \frac{1}{0.981} + \frac{1}{9.81}
  2. Find the reciprocals using mathematical tables.

    From reciprocal tables:
    19.81≈0.1019\frac{1}{9.81} \approx 0.1019
    To find 10.981\frac{1}{0.981}, we can use the relationship 10.981=19.81×10−1=10×19.81\frac{1}{0.981} = \frac{1}{9.81 \times 10^{-1}} = 10 \times \frac{1}{9.81}.
    So, 10.981≈10×0.1019=1.019\frac{1}{0.981} \approx 10 \times 0.1019 = 1.019

  3. Substitute the values and calculate.

    4×1.019+0.10194 \times 1.019 + 0.1019 4.076+0.10194.076 + 0.1019 4.17794.1779

    The evaluated value is 4.1779\boxed{4.1779}.

Part 10· 4 steps

Use laws of indices to work out: (25681)14\left(\frac{256}{81}\right)^{\frac{1}{4}}

  1. Apply the power to both the numerator and the denominator.

    (25681)14=256148114\left(\frac{256}{81}\right)^{\frac{1}{4}} = \frac{256^{\frac{1}{4}}}{81^{\frac{1}{4}}}
  2. Evaluate the fourth root of the numerator.

    25614=2564256^{\frac{1}{4}} = \sqrt[4]{256}
    Since 4×4×4×4=2564 \times 4 \times 4 \times 4 = 256, we have 2564=4\sqrt[4]{256} = 4.

  3. Evaluate the fourth root of the denominator.

    8114=81481^{\frac{1}{4}} = \sqrt[4]{81}
    Since 3×3×3×3=813 \times 3 \times 3 \times 3 = 81, we have 814=3\sqrt[4]{81} = 3.

  4. Substitute the roots back into the fraction.

    43\frac{4}{3}

    The result is ∗43∗\boxed*{\frac{4}{3}*}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp