QuestionIdentify the irrational numbers from the following: a. $\sqrt{42}$ , b. $\sqrt{36}$ , c. $\sqrt{361}$ , d. $\sqrt{18}$ , e. $2-5\sqrt{2}$ , f. $\sqrt{3} \div 2$ . Select all that apply.

Studdy Solution

STEP 1

Assumptions1. An irrational number cannot be expressed as a ratio of two integers. . The square root of a non-perfect square is an irrational number.
3. The square root of a perfect square is a rational number.
4. A rational number subtracted or divided by an irrational number results in an irrational number.

STEP 2

We need to find out if $\sqrt{42}$ is a rational or irrational number. Since42 is not a perfect square, its square root will be an irrational number.

STEP 3

We need to find out if $\sqrt{36}$ is a rational or irrational number. Since36 is a perfect square (6*6), its square root will be a rational number.

STEP 4

We need to find out if $\sqrt{361}$ is a rational or irrational number. Since361 is a perfect square (19*19), its square root will be a rational number.

STEP 5

We need to find out if $\sqrt{18}$ is a rational or irrational number. Since18 is not a perfect square, its square root will be an irrational number.

STEP 6

We need to find out if $2-5 \sqrt{2}$ is a rational or irrational number. Since $\sqrt{2}$ is an irrational number (2 is not a perfect square), $2-5 \sqrt{2}$ will also be an irrational number as it is a rational number (2) subtracted from a product of a rational number and an irrational number.

STEP 7

We need to find out if $\sqrt{3} \div2$ is a rational or irrational number. Since $\sqrt{3}$ is an irrational number (3 is not a perfect square), $\sqrt{3} \div2$ will also be an irrational number as it is an irrational number divided by a rational number.

STEP 8

So, the irrational numbers among the given options are $\sqrt{42}$ , $\sqrt{18}$ , $2-5 \sqrt{2}$ , and $\sqrt{3} \div2$ .
The solution is A. $\sqrt{42}$ , B. $\sqrt{3} \div2$ ,. $2-5 \sqrt{2}$ , and F. $\sqrt{18}$ .

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QuestionIdentify the irrational numbers from the following: a. $\sqrt{42}$ , b. $\sqrt{36}$ , c. $\sqrt{361}$ , d. $\sqrt{18}$ , e. $2-5\sqrt{2}$ , f. $\sqrt{3} \div 2$ . Select all that apply.

Studdy Solution

STEP 1

STEP 2

We need to find out if $\sqrt{42}$ is a rational or irrational number. Since42 is not a perfect square, its square root will be an irrational number.

STEP 3

We need to find out if $\sqrt{36}$ is a rational or irrational number. Since36 is a perfect square (6*6), its square root will be a rational number.

STEP 4

We need to find out if $\sqrt{361}$ is a rational or irrational number. Since361 is a perfect square (19*19), its square root will be a rational number.

STEP 5

We need to find out if $\sqrt{18}$ is a rational or irrational number. Since18 is not a perfect square, its square root will be an irrational number.

STEP 6

We need to find out if $2-5 \sqrt{2}$ is a rational or irrational number. Since $\sqrt{2}$ is an irrational number (2 is not a perfect square), $2-5 \sqrt{2}$ will also be an irrational number as it is a rational number (2) subtracted from a product of a rational number and an irrational number.

STEP 7

We need to find out if $\sqrt{3} \div2$ is a rational or irrational number. Since $\sqrt{3}$ is an irrational number (3 is not a perfect square), $\sqrt{3} \div2$ will also be an irrational number as it is an irrational number divided by a rational number.

STEP 8

So, the irrational numbers among the given options are $\sqrt{42}$ , $\sqrt{18}$ , $2-5 \sqrt{2}$ , and $\sqrt{3} \div2$ .
The solution is A. $\sqrt{42}$ , B. $\sqrt{3} \div2$ ,. $2-5 \sqrt{2}$ , and F. $\sqrt{18}$ .

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QuestionIdentify the irrational numbers from the following: a. 42\sqrt{42}42​, b. 36\sqrt{36}36​, c. 361\sqrt{361}361​, d. 18\sqrt{18}18​, e. 2−522-5\sqrt{2}2−52​, f. 3÷2\sqrt{3} \div 23​÷2. Select all that apply.

Studdy Solution

STEP 1

STEP 2

We need to find out if 42\sqrt{42}42​ is a rational or irrational number. Since42 is not a perfect square, its square root will be an irrational number.

STEP 3

We need to find out if 36\sqrt{36}36​ is a rational or irrational number. Since36 is a perfect square (6*6), its square root will be a rational number.

STEP 4

We need to find out if 361\sqrt{361}361​ is a rational or irrational number. Since361 is a perfect square (19*19), its square root will be a rational number.

STEP 5

We need to find out if 18\sqrt{18}18​ is a rational or irrational number. Since18 is not a perfect square, its square root will be an irrational number.

STEP 6

STEP 7

We need to find out if 3÷2\sqrt{3} \div23​÷2 is a rational or irrational number. Since 3\sqrt{3}3​ is an irrational number (3 is not a perfect square), 3÷2\sqrt{3} \div23​÷2 will also be an irrational number as it is an irrational number divided by a rational number.

STEP 8

So, the irrational numbers among the given options are 42\sqrt{42}42​, 18\sqrt{18}18​, 2−522-5 \sqrt{2}2−52​, and 3÷2\sqrt{3} \div23​÷2.The solution is A. 42\sqrt{42}42​, B. 3÷2\sqrt{3} \div23​÷2,. 2−522-5 \sqrt{2}2−52​, and F. 18\sqrt{18}18​.

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QuestionIdentify the irrational numbers from the following: a. $\sqrt{42}$ , b. $\sqrt{36}$ , c. $\sqrt{361}$ , d. $\sqrt{18}$ , e. $2-5\sqrt{2}$ , f. $\sqrt{3} \div 2$ . Select all that apply.

We need to find out if $\sqrt{42}$ is a rational or irrational number. Since42 is not a perfect square, its square root will be an irrational number.

We need to find out if $\sqrt{36}$ is a rational or irrational number. Since36 is a perfect square (6*6), its square root will be a rational number.

We need to find out if $\sqrt{361}$ is a rational or irrational number. Since361 is a perfect square (19*19), its square root will be a rational number.

We need to find out if $\sqrt{18}$ is a rational or irrational number. Since18 is not a perfect square, its square root will be an irrational number.

We need to find out if $\sqrt{3} \div2$ is a rational or irrational number. Since $\sqrt{3}$ is an irrational number (3 is not a perfect square), $\sqrt{3} \div2$ will also be an irrational number as it is an irrational number divided by a rational number.

So, the irrational numbers among the given options are $\sqrt{42}$ , $\sqrt{18}$ , $2-5 \sqrt{2}$ , and $\sqrt{3} \div2$ .
The solution is A. $\sqrt{42}$ , B. $\sqrt{3} \div2$ ,. $2-5 \sqrt{2}$ , and F. $\sqrt{18}$ .