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Which of the following describes 5\sqrt{5}? Select all that apply.\newlineMulti-select Choices:\newline(A) integer\newline(B) rational number\newline(C) irrational number\newline(D) whole number

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Identify rational and irrational square rootsright chevron icon

Full solution

Q. Which of the following describes 5\sqrt{5}? Select all that apply.\newlineMulti-select Choices:\newline(A) integer\newline(B) rational number\newline(C) irrational number\newline(D) whole number
  1. Evaluate 5\sqrt{5}: Evaluate 5\sqrt{5}.\newline5\sqrt{5} means the number which when multiplied by itself gives 55.\newlineSince no integer or whole number squared gives 55, 5\sqrt{5} is not an integer or a whole number.
  2. Determine Rationality: Determine if 5\sqrt{5} is a rational number.\newlineA rational number can be expressed as a fraction ab\frac{a}{b}, where aa and bb are integers and bb is not zero.\newline5\sqrt{5} cannot be expressed as such a fraction without a decimal or repeating decimal, it is not a rational number.
  3. Check Irrationality: Check if 5\sqrt{5} is an irrational number.\newlineAn irrational number cannot be expressed as a simple fraction.\newlineSince 5\sqrt{5} cannot be expressed as a fraction of integers, it is an irrational number.

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