Is the following number rational or irrational? sqrt20 Choose 1 answer: (A) Rational (B) Irrational

Evaluate square root of 20: Evaluate the square root of 20 to determine if it can be expressed as a fraction of two integers (which would make it rational). sqrt(20) = sqrt(4 * 5) = sqrt(4) * sqrt(5) = 2 * sqrt(5)Determine rationality of sqrt(5): Determine if sqrt(5) is a rational or irrational number. Since 5 is a prime number, it does not have a perfect square root. Therefore, sqrt(5) cannot be expressed as a fraction of two integers.Conclude rationality of sqrt(20): Conclude whether sqrt(20) is rational or irrational based on the previous step. Since sqrt(5) is irrational, and the product of a rational number (2) and an irrational number (sqrt(5)) is irrational, sqrt(20) is irrational.

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Is the following number rational or irrational?

sqrt20
Choose 1 answer:
(A) Rational
(B) Irrational

Is the following number rational or irrational? $\newline$ $\sqrt{20}$ $\newline$ Choose $1$ answer: $\newline$ (A) Rational $\newline$ (B) Irrational

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Math Problems

Algebra 2

Classify rational and irrational numbers

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Q. Is the following number rational or irrational?

\newline

\sqrt{20}

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

Evaluate square root of $20$ : Evaluate the square root of $20$ to determine if it can be expressed as a fraction of two integers (which would make it rational). $\newline$ $\sqrt{20} = \sqrt{4 \times 5}$ $\newline$ $= \sqrt{4} \times \sqrt{5}$ $\newline$ $= 2 \times \sqrt{5}$
Determine rationality of $\sqrt{5}$ : Determine if $\sqrt{5}$ is a rational or irrational number. $\newline$ Since $5$ is a prime number, it does not have a perfect square root. Therefore, $\sqrt{5}$ cannot be expressed as a fraction of two integers.
Conclude rationality of $\sqrt{20}$ : Conclude whether $\sqrt{20}$ is rational or irrational based on the previous step. $\newline$ Since $\sqrt{5}$ is irrational, and the product of a rational number ( $2$ ) and an irrational number ( $\sqrt{5}$ ) is irrational, $\sqrt{20}$ is irrational.