The expression results in a Rational number is √2.√18 .
What is rational number?
A rational number is "a real number which is in the form of p/q, where q ≠ 0.The decimal expansion of any rational number is terminating or repeating".
What is irrational number?
A irrational number is "a real number which is not in the form of p/q, where q ≠ 0.The decimal expansion is non-terminating and non-repeating at any point".
According to the question,
1) √2.√18
=√2.√(9.2)
= √2.3.√2
= 3.2
= 6.
Hence, √2.√18 satisfy the given definition of rational number. The expression √2.√18 is a rational number.
2) √2 + √2 = 2√2 = 2.82842712..... The expression√2 +√2 has decimal expansion which is non-terminating and non-repeating at any point then it is irrational number. hence, √2 + √2 is not a rational number.
5.√5 = 11.1803399.... The expression5√2 has decimal expansion which is non-terminating and non-repeating at any point then it is irrational number. hence, 5√2 is not a rational number.
3√2 + 2√3=7.87831518.... The expression3√2 +2√3 has decimal expansion which is non-terminating and non-repeating at any point then it is irrational number. hence, 3√2+2√3 is not a rational number.
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