The number v is irrational. Which statement about v−8 is true?Choices:(A)v−8 is rational.(B)v−8 is irrational.(C)v−8 can be rational or irrational, depending on the value of v.
Q. The number v is irrational. Which statement about v−8 is true?Choices:(A)v−8 is rational.(B)v−8 is irrational.(C)v−8 can be rational or irrational, depending on the value of v.
Identify Type of Number: Identify whether 8 is a rational or irrational number. 8 is a non-perfect square, which means that its square root cannot be expressed as a simple fraction of two integers. Therefore, 8 is an irrational number.
Properties of Irrational Numbers: Consider the properties of irrational numbers. The sum or difference of an irrational number and a rational number is always irrational. However, the sum or difference of two irrational numbers can be either rational or irrational, depending on the specific numbers involved.
Analyze v−8: Analyze the possible outcomes for v−8. If v is an irrational number that is not related to 8, then v−8 will be irrational because the difference of two unrelated irrational numbers is irrational. If v=8, then v−8 = 8−8 = 0, which is rational. Therefore, v−8 can be rational or irrational, depending on the value of v.
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