Let a be a non-zero rational number. Is (sqrt40)/(a) rational or irrational? Choose 1 answer: (A) Rational (B) Irrational (c) It can be either rational or irrational

Evaluate square root of 40: Evaluate the square root of 40. sqrt(40) = sqrt(4 * 10) = sqrt(4) * sqrt(10) = 2 * sqrt(10)Identify rationality of sqrt(10): Identify whether sqrt(10) is a rational or irrational number. sqrt(10) is not a perfect square, and cannot be expressed as a ratio of two integers. Therefore, sqrt(10) is an irrational number.Division of irrational number by rational number: Consider the division of an irrational number by a non-zero rational number. Dividing an irrational number by a non-zero rational number results in an irrational number. This is because the quotient cannot be expressed as a ratio of two integers.Apply rule to expression (sqrt(40))/a: Apply this rule to the expression (sqrt(40))/a. Since sqrt(40) is irrational (as shown in step 1 and 2), and a is a non-zero rational number, the expression (sqrt(40))/a is irrational.

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Let
a be a non-zero rational number. Is
(sqrt40)/(a) rational or irrational?
Choose 1 answer:
(A) Rational
(B) Irrational
(c) It can be either rational or irrational

Let $a$ be a non-zero rational number. Is $\frac{\sqrt{40}}{a}$ rational or irrational? $\newline$ Choose $1$ answer: $\newline$ (A) Rational $\newline$ (B) Irrational $\newline$ (C) It can be either rational or irrational

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Math Problems

Algebra 2

Classify rational and irrational numbers

Full solution

Q. Let

a

be a non-zero rational number. Is

\frac{\sqrt{40}}{a}

rational or irrational?

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

\newline

Evaluate square root of $40$ : Evaluate the square root of $40$ . $\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2 \times \sqrt{10}$
Identify rationality of $\sqrt{10}$ : Identify whether $\sqrt{10}$ is a rational or irrational number. $\sqrt{10}$ is not a perfect square, and cannot be expressed as a ratio of two integers. Therefore, $\sqrt{10}$ is an irrational number.
Division of irrational number by rational number: Consider the division of an irrational number by a non-zero rational number. $\text{Dividing an irrational number by a non-zero rational number results in an irrational number. This is because the quotient cannot be expressed as a ratio of two integers.}$
Apply rule to expression $(\sqrt{40})/a$ : Apply this rule to the expression $(\sqrt{40})/a$ . $\newline$ Since $\sqrt{40}$ is irrational (as shown in step $1$ and $2$ ), and $a$ is a non-zero rational number, the expression $(\sqrt{40})/a$ is irrational.