Is (sqrt40)/(sqrt5) rational or irrational? Choose 1 answer: (A) Rational (B) Irrational (C) It can be either rational or irrational

Evaluate expression: Evaluate the expression (sqrt40)/(sqrt5) by simplifying the square roots. (sqrt40)/(sqrt5) = sqrt(40/5)Simplify fraction: Simplify the fraction inside the square root. 40/5 = 8Take square root: Take the square root of the simplified fraction. sqrt(8) = sqrt(4 * 2) = sqrt(4) * sqrt(2) = 2 * sqrt(2)Identify rational or irrational: Identify whether 2 * sqrt(2) is a rational or irrational number. Since sqrt(2) is an irrational number and 2 is a rational number, the product of a rational and an irrational number is irrational.

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Is
(sqrt40)/(sqrt5) rational or irrational?
Choose 1 answer:
(A) Rational
(B) Irrational
(C) It can be either rational or irrational

Is $\frac{\sqrt{40}}{\sqrt{5}}$ 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. Is

\frac{\sqrt{40}}{\sqrt{5}}

rational or irrational?

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

\newline

Evaluate expression: Evaluate the expression $(\sqrt{40})/(\sqrt{5})$ by simplifying the square roots. $\newline$ $(\sqrt{40})/(\sqrt{5}) = \sqrt{40/5}$
Simplify fraction: Simplify the fraction inside the square root. $\frac{40}{5} = 8$
Take square root: Take the square root of the simplified fraction. $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2 \times \sqrt{2}$
Identify rational or irrational: Identify whether $2 \times \sqrt{2}$ is a rational or irrational number. $\newline$ Since $\sqrt{2}$ is an irrational number and $2$ is a rational number, the product of a rational and an irrational number is irrational.