Question

Kindly answer this question.....

Answer 1

Sol : ( 1 ) x² = 5

               x = √5.

As √5 is an irrational number , so x represents an irrational number.

Proof : Let √5 is a rational number equals to p/q.Where p and q are co-prime numbers.


 √5 = p/q

By squaring both sides ,

  ( √5 )² = ( p/q )²

  5 = p² / q²

  p² = 5 q²  -------- equation1

Since 5 is a factor of p².So, 5 is also a factor of p.

 Let , p = 5 m.

By substituting the value of p in equation1 ,

  ( 5 m )² = 5 q²

   25 m² = 5 q²

   q² = 25 m² / 5

   q² = 5 m²

Since , 5 is a factor of q² , so 5 is also a factor of q .

So, we got that 5 is a factor of p and q.Hence , our assumption that √5 is a rational number is wrong.So √5 is an irrational number.

Your final answer is that x represents irrational number.


2. y² = 9

    y = √9

   y = ±9.

So ,y = 3 and -3 .It is a rational number.

Proof : The numerators and denominators of 3 and -3 are co - prime numbers.So , it is a rational number.


3. z² = 0.04

   z² = 4 / 100

   z = √ ( 4 / 100 )

   z = √{( 2 x 2  ) / ( 10 x 10 ) }

   z = ±2 / 10

   z = ±1 / 5.

So, z = 1/5 ad -1/5.

Hence , z is a rational number.

Proof : The numerator and denominator of 1 / 5 and -1/5  are co - prime numbers.So, it is a rational number.

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