gh maths solutions

                            1. Real numbers   Exercise-1.4 1 . Prove that following are irrational. (1) 1/√2   (2) √3+√5   (3) 6+√2  (4) √3   (5) 3+2√5 2. Prove that  √p+√q  is an irrational , Where p,q are primes.

                           1. Real numbers   Exerscise-1.3 1. Write the following rational numbers in their decimal form and also state which are terminating and which are non-terminating, repeating decimal.\ (1) 3/8   (2) 229/400   (3) 4(1/5)   (4) 2/11  (5)8/125 2. Without performing division, state whether the following rational numbers will have a terminating decimal form or a non-terminating ,repeating decimal form. (1) 13/3125    (2) 11/12    (3) 64/455    (4) 15/1600    (5) 29/343 (6) 23/2^3.5^2     (7) 129/2^2.5^7.7^5    (8) 9/15    (9) 36/100    (10) 77/210 3. Write the following rationals in decimal form using Theorem1.4 (1) 13/25    (2) 15/16   (3) 23/2^3.5^2   (4) 7218/3^2.5^2 4. Express the following decimals in the form of  p/q and write the prime...

                             1.Real Numbers Exercise-1.1 1 . Use Euclid's algorithm to find the HCF of (1) 900 and 270     (2) 196 and 38220    (3) 1651 and 2032 2. Use division algorithm to show that any positive odd integer is of the form 6q+1 or 6q+3 or 6q+5, where q is some integer. 3. Use division algorithm to show that the square of any positive integer is of form 3p or 3p+1. 4. Use division algorithm to show that the cube of any positive integer is of the form 9m,9m+1 or 9m+8. 5. Show that one and only one out of n,n+2 or n+4 is divisible by    3, where n is any positive integer.

                            1.   Real numbers Exercise-1.2 1.  Express each of the following numbers as a product of its prime factor (1) 140     (2) 156       (3) 3825     (4) 5005      (5)7429 2. Find the LCM and HCF  of the following intergers by the prime factorization method (1) 12,15 and 21        (2)17,23 and 29     (3) 8,9 and 25 (4)72 and 108       (5) 306 and 657 3. Check whether 6^n  can end with the digit 0 for any natural number n. 4. Explain why 7*11*13+13 and 7*6*5*4*3*2*1+5  are composite numbers. 5. How will you show that(17*11*2)+(17*11*5)  is a composite number Explain. 6. Which digit would occupy the units place of resulting number of  6^100.