Is sqrt 2 an irrational number? Choices: (A)yes (B)no

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Is sqrt 2 an irrational number?   Choices: (A)yes (B)no

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Understand irrational numbers:  Step 1: Understand the concept of an irrational number. An irrational number is a number that cannot be expressed as a simple fraction. It's decimal representation is non-terminating and non-repeating.Consider sqrt 2:  Step 2: Consider the number sqrt 2. We need to determine if sqrt 2 can be expressed as a fraction.Attempt fraction expression:  Step 3: Attempt to express sqrt 2 as a fraction. Assume sqrt 2 can be written as a/b, where a and b are integers with no common factors other than 1, and b is not zero.Square to eliminate root:  Step 4: Square both sides to eliminate the square root. (sqrt 2)^2 = (a/b)^2 2 = a^2/b^2 2b^2 = a^2Analyze equation 2b^2 = a^2:  Step 5: Analyze the equation 2b^2 = a^2. This equation implies that a^2 is an even number (since it's 2 times another integer). Therefore, a must also be even (since only even numbers squared give even results).Substitute a = 2k:  Step 6: If a is even, there exists an integer k such that a = 2k. Substitute a = 2k into the equation: 2b^2 = (2k)^2 2b^2 = 4k^2 b^2 = 2k^2Follow b^2 = 2k^2:  Step 7: From b^2 = 2k^2, it follows that b^2 is also even, and hence b is even. This contradicts our initial assumption that a and b have no common factors other than 1, as both are divisible by 2.Conclude sqrt 2 is irrational:  Step 8: Conclude that sqrt 2 cannot be expressed as a fraction of two integers. Since our assumption led to a contradiction, sqrt 2 must be irrational.

Is $\sqrt{2}$ an irrational number? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Is $\sqrt{2}$ an irrational number? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no