State whether the given exponent is true or false. is an irrational number.

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The given exponent is true.Concept- Here, we determine if the numbers 3 and 2 meet the criteria for being irrational numbers by referring to the concept of irrational numbers. Then, to demonstrate that the total is irrational, utilize the property of the sum of two irrational integers.The value of an irrational number is represented in decimal form as non-recurring, non-repeating, and non-terminating. . Irrational numbers are any figures that are not rational figures. Examples are 2,, pi, etc.We have to prove that  is an irrational number.We will check separately for the values of  and  and then check for their sum.We know a number that can be written in the form  A rational number is one where is non-zero and both the numerator and denominator are integers, and whose decimal representation is either ending or recurring.Irrational numbers are any figures that are not rational figures.We know  is an irrational number because it cannot be represented in the form , also if we try to find the square root of 2 in decimal from then,  where the decimal representation is nonrecurring, non-repeating and non-terminating.We are aware that depending on the two numbers, the sum of two irrational numbers might either be rational or irrational. The consequent will be rational if the numbers are comparable, that is, they have the same number as the square root, otherwise, the sum will be irrational if the numbers are different (in the least and simplest form) beneath the square root.Since both the numbers  and  are irrational numbers and the numbers under the square root are different so there is no chance of terms to cancel each other. So, the sum of  and  will be an irrational number. is an irrational numberHence, the given exponent is true.

State whether the given exponent is true or false.

is an irrational number.

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