Is (36)/(25)*sqrt11 rational or irrational? Choose 1 answer: (A) Rational (B) Irrational (C) It can be either rational or irrational

Evaluate expression: Evaluate the expression (36)/(25)*sqrt(11). (36)/(25) is a rational number because it can be expressed as a fraction of two integers. However, sqrt(11) is an irrational number because it cannot be expressed as a fraction of two integers; the square root of a non-perfect square is always irrational.Nature of product: Determine the nature of the product of a rational number and an irrational number. The product of a rational number and an irrational number is always irrational. This is because if the product were rational, then you could express the irrational number as the quotient of the rational product and the rational number, which is not possible.Apply rule: Apply the rule to the given expression. Since (36)/(25) is rational and sqrt(11) is irrational, their product (36)/(25)*sqrt(11) must be irrational.

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Is
(36)/(25)*sqrt11 rational or irrational?
Choose 1 answer:
(A) Rational
(B) Irrational
(C) It can be either rational or irrational

Is $\frac{36}{25}\sqrt{11}$ 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{36}{25}\sqrt{11}

rational or irrational?

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

\newline

Evaluate expression: Evaluate the expression $(\frac{36}{25})\sqrt{11}$ . $(\frac{36}{25})$ is a rational number because it can be expressed as a fraction of two integers. However, $\sqrt{11}$ is an irrational number because it cannot be expressed as a fraction of two integers; the square root of a non-perfect square is always irrational.
Nature of product: Determine the nature of the product of a rational number and an irrational number. $\newline$ The product of a rational number and an irrational number is always irrational. $\newline$ This is because if the product were rational, then you could express the irrational number as the quotient of the rational product and the rational number, which is not possible.
Apply rule: Apply the rule to the given expression. $\newline$ Since $(\frac{36}{25})$ is rational and $\sqrt{11}$ is irrational, their product $(\frac{36}{25})\cdot\sqrt{11}$ must be irrational.