Question

check whether under root 45 is a rational number or irrational number ​

Answer 1

Answer:

it is an irrational number.

Step-by-step explanation:

$\sqrt{45} = 3 \sqrt{5} \\ hence \: it \: is \: an \: irrational \: number$

Answer 2

Answer:

it is................

let it be rational.....

therefore, √45=a/b, where a and b are prime no:

⇒45b²=a²>>>>>>>>(1)

let a=45c

so, (45c)²=45b²

⇒45c²=b²>>>>>>>>>>>>>>>(2)

But from 1 and 2 we get that b is a composite no: but our assumption says it is prime....

thus our assumption is wrong...

thus √45 is irrational..............

Proof:

√45=3√5 and √5 is irratioonal thus any no: multiplied with irrational no is irrational......

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