Question

examine whether (√2+1/√2)^2 is a rational number or an irrational number.

Answer 1

Answer:

(√2+1/√2)²

=[(√2)²+2√2+1]/2

=(2+√2+1)/2

=1+√2+1/2

=3/2+√2

So it is an irrational no.

Answer 2

Concept

Rational number is the number that can be represented in the form of p/q when q ≠ 0.Irrational numbers are the numbers that can't be represented in  simple fraction. Sum of rational and irrational number is an irrational number.

Find

To examine whether (√2+1/√2)² is a rational or irrational number.

Solution

(√2+1/√2)²

Using (a+b)² = a²+b²+2ab

(√2+1/√2)² =  (√2)² + (1/√2)² + 2

= 2 + 1/2 + 2

= 4 + 1/2

= 9/2

Hence (√2+1/√2)² = 9/2 is a rational number.

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