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Jakob is working on his math homework. he decides that the sum of the expression os 1/3 6 square root of 5/7 must be rational because it us a fraction. is jakob correct? explain your reasoning.

User Mitkp
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Final answer:

Jakob is incorrect; the presence of the square root of a non-square rational number makes the sum irrational, despite the initial rational number factors.

Step-by-step explanation:

Jakob is not correct in assuming that the sum of the expression 1/3 x 6 x √(5/7) must be rational just because it appears as a fraction. Rational numbers are numbers that can be expressed as the quotient or fraction p/q of two integers, where p and q are integers and q is not zero. However, the presence of the square root of 5/7 in the expression complicates things. While 5/7 is a rational number, the square root of a non-square rational number is irrational. Multiplying an irrational number by a rational number, in this case 1/3 x 6, results in an irrational number. Thus, Jakob's sum is irrational.

User Gurmanjot Singh
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