Let 4-√3 be rational So, 4-√3 = p/q where p and q are co-prime integers and q not equal to 0. √3= 4-p/q √3=4q-p/q Since 4 ,p and q are integers. So,4q-p/p is rational (integer/integer).Where as √3 is irrational. It contradicts our assumption.so,4-√3 is irrational.
210=2×3×5×755=5×11So,HCF=5
Let us possible 4root 3 is a rational number and it\’s simplest form be a/b now, 4root 3 =a/b so, root 3 = a/4b for any positive value of a and b gives a /4b is a rational number. But it contradict the fact that root 3 is irrational. The contradiction arises by assuming the fact that 4 root 3 is irrational. Hence, 4 root 3 is an irrational number.
Prove that 4-√3 is ir-rational