prove that 5-2√3 is an irrational
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☆Let us assume that 5-2root 3 is rational number .
5-2root 3=p/q.
[where p and q are rational numbers and q is not equal to zero. ]
-2root3=p/q-5
-2root3 =p-5q/q.
-root3=p-5q/q
root3= -[p-5q/q]
root 3= -p+5q/2q.
☆Irrational is not equal to rational.
☆LHS is not equal to RHS.
☆As root 3 is irrational.
☆Thus, we can say that 5-2root3 is also an irrational number.
Hope it helps. ☆☆
5-2root 3=p/q.
[where p and q are rational numbers and q is not equal to zero. ]
-2root3=p/q-5
-2root3 =p-5q/q.
-root3=p-5q/q
root3= -[p-5q/q]
root 3= -p+5q/2q.
☆Irrational is not equal to rational.
☆LHS is not equal to RHS.
☆As root 3 is irrational.
☆Thus, we can say that 5-2root3 is also an irrational number.
Hope it helps. ☆☆
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