Issqrt 8anirrationalnumber? Choices: (A)yes (B)no

Understand irrational numbers: Understand what an irrational number is. An irrational number is a number that cannot be expressed as a simple fraction - that is, the ratio of two integers. It is a number that has a non-repeating, non-terminating decimal expansion.Simplify sqrt(8): Express sqrt(8) in its simplest radical form. Sqrt(8) can be simplified by recognizing that 8 is 4 times 2, and 4 is a perfect square. Therefore, sqrt(8) = sqrt(4 * 2) = sqrt(4) * sqrt(2) = 2 * sqrt(2).Determine sqrt(2): Determine if sqrt(2) is an irrational number. Sqrt(2) is known to be an irrational number because it cannot be expressed as a fraction of two integers. Its decimal expansion is non-repeating and non-terminating.Conclude sqrt(8): Conclude whether sqrt(8) is an irrational number. Since sqrt(8) simplifies to 2 * sqrt(2) and we know that sqrt(2) is irrational, the product of a rational number (2) and an irrational number (sqrt(2)) is also irrational. Therefore, sqrt(8) is an irrational number.

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Is $\sqrt{8}$ an irrational number? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Algebra 2

Find trigonometric ratios using reference angles

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Q. Is

\sqrt{8}

an irrational number?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Understand irrational numbers: Understand what an irrational number is. An irrational number is a number that cannot be expressed as a simple fraction - that is, the ratio of two integers. It is a number that has a non-repeating, non-terminating decimal expansion.
Simplify $\sqrt{8}$ : Express $\sqrt{8}$ in its simplest radical form. $\newline$ $\sqrt{8}$ can be simplified by recognizing that $8$ is $4$ times $2$ , and $4$ is a perfect square. Therefore, $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2 \times \sqrt{2}$ .
Determine $\sqrt{2}$ : Determine if $\sqrt{2}$ is an irrational number. $\newline$ $\sqrt{2}$ is known to be an irrational number because it cannot be expressed as a fraction of two integers. Its decimal expansion is non-repeating and non-terminating.
Conclude $\sqrt{8}$ : Conclude whether $\sqrt{8}$ is an irrational number. $\newline$ Since $\sqrt{8}$ simplifies to $2 \times \sqrt{2}$ and we know that $\sqrt{2}$ is irrational, the product of a rational number ( $2$ ) and an irrational number ( $\sqrt{2}$ ) is also irrational. Therefore, $\sqrt{8}$ is an irrational number.