Question

Prove 3-root5 is irrational prove it by identity

Answer 1

Let us assume that 3-√5 is a rational number i.e. 3-√5=r , where"r" is a rational number.

Squaring to both sides, we get

(3-√5)²=r²

3²-2×3×√5+(√5)²=r²

9-6√5+5=r²

14-6√5=r²

-6√5=r²-14

√5=r²-14

-6

Here, we find that LHS is irrational .But RHS is rational.

This contradicts the fact that 3-√5 is rational.

So , our assumption was wrong.

Hence, 3-√5 is an irrational number.

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Answer 2

Answer:

Step-by-step explanation:

Let us assume that 3-√5 is a rational number i.e. 3-√5=r , where"r" is a rational number.

Squaring to both sides, we get

(3-√5)²=r²

3²-2×3×√5+(√5)²=r²

9-6√5+5=r²

14-6√5=r²

-6√5=r²-14

√5=r²-14

-6

Here, we find that LHS is irrational .But RHS is rational.

This contradicts the fact that 3-√5 is rational.

So , our assumption was wrong.

Hence, 3-√5 is an irrational number