Is the following number rational or irrational? sqrt50 Choose 1 answer: (A) Rational (B) Irrational

Evaluate square root of 50: Evaluate the square root of 50. sqrt(50) = sqrt(25 * 2) = sqrt(25) * sqrt(2) = 5 * sqrt(2)Identify irrationality 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 nature of product: Determine the nature of the product of a rational number (5) and an irrational number (sqrt(2)). The product of a non-zero rational number and an irrational number is always irrational.Conclude rationality of sqrt(50): Conclude whether sqrt(50) is rational or irrational. Since sqrt(50) is equal to 5 * sqrt(2), and we have established that sqrt(2) is irrational, sqrt(50) must also be irrational.

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Is the following number rational or irrational?

sqrt50
Choose 1 answer:
(A) Rational
(B) Irrational

Is the following number rational or irrational? $\newline$ $\sqrt{50}$ $\newline$ 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{50}

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

Evaluate square root of $50$ : Evaluate the square root of $50$ . $\newline$ $\sqrt{50}$ $\newline$ = $\sqrt{25 \times 2}$ $\newline$ = $\sqrt{25}$ $\times$ $\sqrt{2}$ $\newline$ = $5 \times \sqrt{2}$
Identify irrationality 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 nature of product: Determine the nature of the product of a rational number $5$ and an irrational number $\sqrt{2}$ . $\newline$ The product of a non-zero rational number and an irrational number is always irrational.
Conclude rationality of $\sqrt{50}$ : Conclude whether $\sqrt{50}$ is rational or irrational. $\newline$ Since $\sqrt{50}$ is equal to $5 \times \sqrt{2}$ , and we have established that $\sqrt{2}$ is irrational, $\sqrt{50}$ must also be irrational.