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The side length of a square seat cushion is 70⎯⎯⎯⎯√ square inches. Determine whether the side length is rational or irrational....Asked by Him
The side length of a square seat cushion is 70⎯⎯⎯⎯√
square inches. Determine whether the side length is rational or irrational. Then explain your reasoning.
square inches. Determine whether the side length is rational or irrational. Then explain your reasoning.
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GPT 3.5
To determine whether the side length of the square cushion is rational or irrational, we need to consider whether the value of √70 is rational or irrational.
If √70 is rational, then it can be expressed as a fraction p/q, where p and q are integers with no common factors other than 1. However, if √70 is irrational, it cannot be expressed as a fraction and has an infinite number of non-repeating decimal places.
To determine the nature of √70, we can consider its prime factors.
The prime factorization of 70 is 2 * 5 * 7.
Since there is no perfect square that can be multiplied by 2, 5, or 7 to result in 70, we can conclude that √70 is not a rational number.
Therefore, the side length of the square cushion (√70) is irrational.
If √70 is rational, then it can be expressed as a fraction p/q, where p and q are integers with no common factors other than 1. However, if √70 is irrational, it cannot be expressed as a fraction and has an infinite number of non-repeating decimal places.
To determine the nature of √70, we can consider its prime factors.
The prime factorization of 70 is 2 * 5 * 7.
Since there is no perfect square that can be multiplied by 2, 5, or 7 to result in 70, we can conclude that √70 is not a rational number.
Therefore, the side length of the square cushion (√70) is irrational.
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