Question

check whether (√3+√2)^2 is a rational or an irrational number​

Answer 1

Answer:

Rational number

Step-by-step explanation:

First we have to find the expanded form of (3 + 2√2)(3 - 2√2).

Here the result is 1, which is a rational number, isn't it?

1 can be written as a fraction, means in p/q form, as the following:

1 = 1/1 = 2/2 = 3/3 = 4/4 = 5/5 = 6/6 = 7/7 = 8/8 = 9/9 = 10/10......

Thus, we found that  (3 + 2√2)(3 - 2√2)  is a rational number because it results in 1.

Hence proved that  (3 + 2√2)(3 - 2√2)  is not an irrational number.

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Answer 2

Answer: By using the identity,

(a+b)^2 = a^2+b^2+2ab

(√3+√2)^2 = (√3)^2+(√2)^2+2×√3×√2

= 3+2+2√6

= 5+2√6

As 2√6 is an irrational number, (√3+√2)^2 is also an Irrational Number.