Real Numbers

Question 1
Find the rational number between root 2 and root 3?

Question 2
 Tow positive integers a and b can be written as a = x^3y^2 and b= xy^3. x, y are prime numbers, then LCM (a, b).

Question 3
Find the HCF of 1260 and 7344 using Euclid's algorithm.

Question 4
Show that every positive integer is of the form 4q+1 or9 4q+3 where q is some integer.

Question 5
Prove that root 2 is an irrational number.

Question 6
Prove that 2+(root 3/5) is an irrational number, given that root 3 is an irrational number.

Question 7
Prove that 2+5 root 3 is an irrational number.

Question 8
What is the HCF of smallest prime number and the smallest composite number?

Question 9
Given that root 2 is irrrational, prove that (5+3 root 2) is an irrational number.

Question 10
Find HCFand LCM of 404 and 96 and verifiy that HCF*LCM = Product of the two given numbers.

Question 11
Write whether ( 2 root 45 + 3 root 20)/( 2 root 5 ) on simplification gives an irrational or a roational number.

Qustion 12
Given that root 3 is an irrational number, prove that (2+ root 3) is an irrational number.

Question 13
Using Euclid's dvision algorithm find the HCF ofthe number 867 and 255.

Question 14
Two tankers contain 850 litres and 680 litres of petrol respectively. Find the maximum capacity of a container which can measure the petrol of either tanker in exact number of times.

Question 15
Find the value of: (-1)^n + (-1)^2n + (-1)^2n+1 + (-1)^4n+2, where n is  any positive odd integer.

Question 16
Find whether the decimal expension of 13/64 is terminating or non-terminating decimal. If it teminates find the number of decimal places its decimal expension has.

Question 17
Find whether the number 3*5*13*46+23 is prime number or composite number.

Question 18
Prove that the product of any three consecutive positive integer is divisible by 6.

Question 19
Apply Euclid's division algorithm to find the HCF of (4052 and 420)

Question 20
Prove that root 3 + root 5 is an irrational number.

Question 21
Three bells ring at an interval of 12 minutes, 15 minutes, and  18 minutes respectivily. If they start ringing togather, after what time will they ring togather.

Question 22
If the HCFof  144 and 180 is expressed in the form of 3m - 3, find the value of m.

Question 23
Determine the value of p and q so that the prime factorisation of  2520 is expressible as 2^3 * 3^p * q * 7.

Question 24
Show that 2 root 2 is an irrational number.

Question 25
Show that any positive integer is in the form of 4m + 1, or 4m + 3 where m is some integer.

Question 26
Show that raciprocal of 3 + 2 root 2 is an irrational number.