Let a be a non-zero rational number. Is a*sqrt8 rational or irrational? Choose 1 answer: (A) Rational (B) Irrational (C) It can be either rational or irrational

Evaluate square root of 8: Evaluate the square root of 8. √8 = √(4 * 2) √8 = √4 * √2 √8 = 2√2Identify nature of square root of 2: Identify whether √2 is a rational or irrational number. √2 cannot be expressed as a fraction of two integers, hence it is an irrational number.Multiply rational number by 2√2: Multiply a non-zero rational number 'a' by the irrational number 2√2. a * 2√2 Since 'a' is rational and 2√2 is irrational, their product will be irrational.Conclude nature of a * √8: Conclude whether a * √8 is rational or irrational. Since the product of a rational number and an irrational number is always irrational, a * √8 is irrational.

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Let
a be a non-zero rational number. Is
a*sqrt8 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 $a\sqrt{8}$ 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

a\sqrt{8}

rational or irrational?

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

\newline

Evaluate square root of $8$ : Evaluate the square root of $8$ . $\newline$ $\sqrt{8} = \sqrt{(4 \cdot 2)}$ $\newline$ $\sqrt{8} = \sqrt{4} \cdot \sqrt{2}$ $\newline$ $\sqrt{8} = 2\sqrt{2}$
Identify nature of square root of $2$ : Identify whether $\sqrt{2}$ is a rational or irrational number. $\newline$ $\sqrt{2}$ cannot be expressed as a fraction of two integers, hence it is an irrational number.
Multiply rational number by $2\sqrt{2}$ : Multiply a non-zero rational number ' $a$ ' by the irrational number $2\sqrt{2}$ . $\newline$ $a \times 2\sqrt{2}$ $\newline$ Since ' $a$ ' is rational and $2\sqrt{2}$ is irrational, their product will be irrational.
Conclude nature of a $\times \sqrt{8}$ : Conclude whether $a \times \sqrt{8}$ is rational or irrational. $\newline$ Since the product of a rational number and an irrational number is always irrational, $a \times \sqrt{8}$ is irrational.