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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.
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16 stepsPart 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.
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:Identify the largest and smallest prime numbers from the list.
Smallest prime number = 101
Largest prime number = 113Calculate the product of the largest and smallest prime numbers.
Product =
The product of the largest and smallest prime numbers is .
Part 7· 4 steps
The shorter sides of a right angled triangle are 1 m and 2 m respectively. Its longest side is m. Classify 1, 2 and as rational or irrational numbers.
Define rational and irrational numbers.
A rational number can be expressed as a fraction where and are integers and .
An irrational number cannot be expressed as a simple fraction; its decimal representation is non-terminating and non-repeating.Classify 1.
1 can be written as . Therefore, 1 is a rational number.
Classify 2.
2 can be written as . Therefore, 2 is a rational number.
Classify .
Since 5 is not a perfect square, cannot be expressed as a simple fraction. Its decimal representation is non-terminating and non-repeating (2.23606...). Therefore, 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.
Determine the fraction of the journey covered in 1 hour.
If the total journey takes 5 hours, then in 1 hour, the train covers of the journey.
Use reciprocal tables to find the value of .
Looking up the reciprocal of 5 in a reciprocal table gives:
The fraction of the journey covered in 1 hour is .
Part 94.1779
Use mathematical tables to evaluate:
Rewrite the expression using reciprocals.
Find the reciprocals using mathematical tables.
From reciprocal tables:
To find , we can use the relationship .
So,Substitute the values and calculate.
The evaluated value is .
Part 10· 4 steps
Use laws of indices to work out:
Apply the power to both the numerator and the denominator.
Evaluate the fourth root of the numerator.
Since , we have .Evaluate the fourth root of the denominator.
Since , we have .Substitute the roots back into the fraction.
The result is .
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