Is the following number rational or irrational? sqrt45 Choose 1 answer: (A) Rational (B) Irrational

Evaluate Square Root of 45: Evaluate the square root of 45 to determine if it can be expressed as a fraction of two integers (which would make it rational). sqrt(45) = sqrt(9 * 5) = sqrt(9) * sqrt(5) = 3 * sqrt(5)Determine Rationality of Square Root of 5: Determine if sqrt(5) is a rational or irrational number. sqrt(5) cannot be expressed as a fraction of two integers because 5 is not a perfect square. Therefore, sqrt(5) is an irrational number.Product of Rational and Irrational Numbers: Since the product of a rational number (3) and an irrational number (sqrt(5)) is always irrational, sqrt(45) is irrational.

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Is the following number rational or irrational?

sqrt45
Choose 1 answer:
(A) Rational
(B) Irrational

Is the following number rational or irrational? $\newline$ $\sqrt{45}$ $\newline$ 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{45}

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

Evaluate Square Root of $45$ : Evaluate the square root of $45$ to determine if it can be expressed as a fraction of two integers (which would make it rational). $\newline$ $\sqrt{45} = \sqrt{9 \times 5}$ $\newline$ $= \sqrt{9} \times \sqrt{5}$ $\newline$ $= 3 \times \sqrt{5}$
Determine Rationality of Square Root of $5$ : Determine if $\sqrt{5}$ is a rational or irrational number. $\sqrt{5}$ cannot be expressed as a fraction of two integers because $5$ is not a perfect square. Therefore, $\sqrt{5}$ is an irrational number.
Product of Rational and Irrational Numbers: Since the product of a rational number $3$ and an irrational number $\sqrt{5}$ is always irrational, $\sqrt{45}$ is irrational.