1.

Show that 2−3√5 is an irrational number

Answer»

Step-by-step explanation:

LET X=2−3 √5

be a RATIONAL number.

3 √5 =2−x

√5 = 3

2−x

SINCE x is rational, 2-x is rational and hence

3

2−x is also rational number

⇒

√5

is a rational numbers, which is a contradiction.

Hence 2−3√5

must be an irrational number.

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