Select all the numbers that are irrational. Multi-select Choices: (A)sqrt 39 (B)sqrt 36 (C)sqrt 55 (D)sqrt 40 (E)sqrt 49

Check Irrationality of sqrt(39): Step 1: Determine if sqrt(39) is irrational. sqrt(39) cannot be simplified to a perfect square root, meaning it does not result in a whole number. Therefore, it is an irrational number.Check Irrationality of sqrt(36): Step 2: Check if sqrt(36) is irrational. sqrt(36) equals 6, which is a whole number. Since it can be expressed as a fraction (6/1), it is not an irrational number.Check Irrationality of sqrt(55): Step 3: Evaluate if sqrt(55) is irrational. Like sqrt(39), sqrt(55) also cannot be simplified to a perfect square root and does not result in a whole number. Hence, it is an irrational number.Check Irrationality of sqrt(40): Step 4: Assess if sqrt(40) is irrational. sqrt(40) simplifies to 2*sqrt(10), which is not a whole number. This means it is an irrational number.Check Irrationality of sqrt(49): Step 5: Determine if sqrt(49) is irrational. sqrt(49) equals 7, which is a whole number. Since it can be expressed as a fraction (7/1), it is not an irrational number.

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Select all the numbers that are irrational. $\newline$ Multi-select Choices: $\newline$ (A) $\sqrt{39}$ $\newline$ (B) $\sqrt{36}$ $\newline$ (C) $\sqrt{55}$ $\newline$ (D) $\sqrt{40}$ $\newline$ (E) $\sqrt{49}$

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Math Problems

Grade 8

Checkpoint: Rational and irrational numbers

Full solution

Q. Select all the numbers that are irrational.

\newline

Multi-select Choices:

\newline

(A)

\sqrt{39}

\newline

(B)

\sqrt{36}

\newline

(C)

\sqrt{55}

\newline

(D)

\sqrt{40}

\newline

(E)

\sqrt{49}

Check Irrationality of $\sqrt{39}$ : Step $1$ : Determine if $\sqrt{39}$ is irrational. $\newline$ $\sqrt{39}$ cannot be simplified to a perfect square root, meaning it does not result in a whole number. Therefore, it is an irrational number.
Check Irrationality of $\sqrt{36}$ : Step $2$ : Check if $\sqrt{36}$ is irrational. $\newline$ $\sqrt{36}$ equals $6$ , which is a whole number. Since it can be expressed as a fraction ( $\frac{6}{1}$ ), it is not an irrational number.
Check Irrationality of $\sqrt{55}$ : Step $3$ : Evaluate if $\sqrt{55}$ is irrational. $\newline$ Like $\sqrt{39}$ , $\sqrt{55}$ also cannot be simplified to a perfect square root and does not result in a whole number. Hence, it is an irrational number.
Check Irrationality of $\sqrt{40}$ : Step $4$ : Assess if $\sqrt{40}$ is irrational. $\newline$ $\sqrt{40}$ simplifies to $2\cdot\sqrt{10}$ , which is not a whole number. This means it is an irrational number.
Check Irrationality of $\sqrt{49}$ : Step $5$ : Determine if $\sqrt{49}$ is irrational. $\newline$ $\sqrt{49}$ equals $7$ , which is a whole number. Since it can be expressed as a fraction ( $7/1$ ), it is not an irrational number.