Question

A student claims that the sum of a rational number and an irrational number is always irrational. Is the claim correct? No. The claim is incorrect because 2 + √ 4 = 2 + 2 = 4 , and 4 is a rational number. No. The claim is incorrect because 2 plus square root of 4 is equal to 2 plus 2 is equal to 4, and 4 is a rational number. No. The claim is incorrect because 2 + 1 √ 4 = 2 + 1 2 = 5 2 , and 5 2 is a rational number. No. The claim is incorrect because 2 plus the fraction with numerator 1 and denominator square root of 4 is equal to 2 plus 1 half is equal to 5 halves, and 5 halves is a rational number. Yes. The claim is correct because 3 π + 4 π = 7 π , and 7 π is an irrational number. Yes. The claim is correct because 3 pi plus 4 pi is equal to 7 pi, and 7 pi is an irrational number. Yes. The claim is correct because √ 16 + π = 4 + π , and 4 + π is an irrational number. Yes. The claim is correct because square root of 16 plus pi is equal to 4 plus pi, and 4 plus pi is an irrational number.

Answer 1

The correct option regarding whether the sum of a rational number and an irrational number is always irrational is given by:

Yes. The claim is correct because √ 16 + π = 4 + π , and 4 + π is an irrational number.

What are rational and irrational numbers?

• Rational numbers are numbers that can be represented by fractions, such as terminating decimals.

• Irrational numbers are numbers that cannot be represented by fractions, such as non-terminating decimals and non-exact roots.

The sum of a terminating decimal with a non-terminating decimal always results in a non terminating decimal, that is, the sum of a rational number with an irrational number is always irrational, and the correct option is given by:

Yes. The claim is correct because √ 16 + π = 4 + π , and 4 + π is an irrational number.

More can be learned about rational and irrational numbers at brainly.com/question/17232771

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