Is the following number rational or irrational? sqrt200 Choose 1 answer: (A) Rational (B) Irrational

Evaluate prime factorization: Evaluate the prime factorization of 200 to simplify sqrt(200). 200 = 2 * 2 * 2 * 5 * 5 = (2^3) * (5^2)Extract perfect squares: Extract perfect squares from under the square root. sqrt(200) = sqrt((2^3) * (5^2)) = sqrt((2^2) * 2 * (5^2)) = sqrt(4) * sqrt(2) * sqrt(25) = 2 * sqrt(2) * 5 = 10 * sqrt(2)Identify rationality of sqrt(2): Identify whether sqrt(2) is a rational or irrational number. sqrt(2) is known to be an irrational number because it cannot be expressed as a fraction of two integers.Determine rationality of product: Determine the rationality of the product of a rational number and an irrational number. The product of a non-zero rational number (10) and an irrational number (sqrt(2)) is irrational.

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Is the following number rational or irrational?

sqrt200
Choose 1 answer:
(A) Rational
(B) Irrational

Is the following number rational or irrational? $\newline$ $\sqrt{200}$ $\newline$ Choose $1$ answer: $\newline$ (A) Rational $\newline$ (B) Irrational

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Algebra 2

Classify rational and irrational numbers

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Q. Is the following number rational or irrational?

\newline

\sqrt{200}

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

Evaluate prime factorization: Evaluate the prime factorization of $200$ to simplify $\sqrt{200}$ . $\newline$ $200 = 2 \times 2 \times 2 \times 5 \times 5$ $\newline$ $= (2^3) \times (5^2)$
Extract perfect squares: Extract perfect squares from under the square root. $\newline$ $\sqrt{200} = \sqrt{(2^3) \cdot (5^2)}$ $\newline$ $= \sqrt{(2^2) \cdot 2 \cdot (5^2)}$ $\newline$ $= \sqrt{4} \cdot \sqrt{2} \cdot \sqrt{25}$ $\newline$ $= 2 \cdot \sqrt{2} \cdot 5$ $\newline$ $= 10 \cdot \sqrt{2}$
Identify rationality of $\sqrt{2}$ : Identify whether $\sqrt{2}$ is a rational or irrational number. $\newline$ $\sqrt{2}$ is known to be an irrational number because it cannot be expressed as a fraction of two integers.
Determine rationality of product: Determine the rationality of the product of a rational number and an irrational number. $\newline$ The product of a non-zero rational number $10$ and an irrational number $\sqrt{2}$ is irrational.