QuestionChoose the irrational number from the options: a. $\sqrt{25}$ b. $\sqrt{49}$ c. $\frac{3}{4}$ d. $\sqrt{\frac{8}{7}}$

Studdy Solution

STEP 1

Assumptions1. An irrational number is a number that cannot be expressed as a ratio of two integers. . The square root of a perfect square is a rational number.
3. A fraction of two integers is a rational number.

STEP 2

Evaluate each option to determine if it is a rational or irrational number.
a. $\sqrt{25}$

STEP 3

Calculate the square root of25.
$\sqrt{25} =5$

STEP 4

Since is a rational number, option a is not the answer.
b. $\sqrt{49}$

STEP 5

Calculate the square root of49.
$\sqrt{49} =7$

STEP 6

Since is a rational number, option b is not the answer.
c. $\frac{3}{4}$

STEP 7

Since $\frac{3}{4}$ is a fraction of two integers, it is a rational number. Therefore, option c is not the answer.
d. $\sqrt{\frac{}{7}}$

STEP 8

Calculate the square root of $\frac{8}{7}$ .
Since $\frac{8}{7}$ is not a perfect square, its square root will be an irrational number.
Therefore, the answer is option d, $\sqrt{\frac{8}{7}}$ .

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QuestionChoose the irrational number from the options: a. $\sqrt{25}$ b. $\sqrt{49}$ c. $\frac{3}{4}$ d. $\sqrt{\frac{8}{7}}$

Studdy Solution

STEP 1

Assumptions1. An irrational number is a number that cannot be expressed as a ratio of two integers. . The square root of a perfect square is a rational number.
3. A fraction of two integers is a rational number.

STEP 2

Evaluate each option to determine if it is a rational or irrational number.
a. $\sqrt{25}$

STEP 3

Calculate the square root of25.
$\sqrt{25} =5$

STEP 4

Since is a rational number, option a is not the answer.
b. $\sqrt{49}$

STEP 5

Calculate the square root of49.
$\sqrt{49} =7$

STEP 6

Since is a rational number, option b is not the answer.
c. $\frac{3}{4}$

STEP 7

Since $\frac{3}{4}$ is a fraction of two integers, it is a rational number. Therefore, option c is not the answer.
d. $\sqrt{\frac{}{7}}$

STEP 8

Calculate the square root of $\frac{8}{7}$ .
Since $\frac{8}{7}$ is not a perfect square, its square root will be an irrational number.
Therefore, the answer is option d, $\sqrt{\frac{8}{7}}$ .

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QuestionChoose the irrational number from the options: a. 25\sqrt{25}25​ b. 49\sqrt{49}49​ c. 34\frac{3}{4}43​ d. 87\sqrt{\frac{8}{7}}78​​

Studdy Solution

STEP 1

Assumptions1. An irrational number is a number that cannot be expressed as a ratio of two integers. . The square root of a perfect square is a rational number.3. A fraction of two integers is a rational number.

STEP 2

Evaluate each option to determine if it is a rational or irrational number.a. 25\sqrt{25}25​

STEP 3

Calculate the square root of25.25=5\sqrt{25} =525​=5

STEP 4

Since is a rational number, option a is not the answer.b. 49\sqrt{49}49​

STEP 5

Calculate the square root of49.49=7\sqrt{49} =749​=7

STEP 6

Since is a rational number, option b is not the answer.c. 34\frac{3}{4}43​

STEP 7

Since 34\frac{3}{4}43​ is a fraction of two integers, it is a rational number. Therefore, option c is not the answer.d. 7\sqrt{\frac{}{7}}7​​

STEP 8

Calculate the square root of 87\frac{8}{7}78​.Since 87\frac{8}{7}78​ is not a perfect square, its square root will be an irrational number.Therefore, the answer is option d, 87\sqrt{\frac{8}{7}}78​​.

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QuestionChoose the irrational number from the options: a. $\sqrt{25}$ b. $\sqrt{49}$ c. $\frac{3}{4}$ d. $\sqrt{\frac{8}{7}}$

Assumptions1. An irrational number is a number that cannot be expressed as a ratio of two integers. . The square root of a perfect square is a rational number.
3. A fraction of two integers is a rational number.

Evaluate each option to determine if it is a rational or irrational number.
a. $\sqrt{25}$

Calculate the square root of25.
$\sqrt{25} =5$

Since is a rational number, option a is not the answer.
b. $\sqrt{49}$

Calculate the square root of49.
$\sqrt{49} =7$

Since is a rational number, option b is not the answer.
c. $\frac{3}{4}$

Since $\frac{3}{4}$ is a fraction of two integers, it is a rational number. Therefore, option c is not the answer.
d. $\sqrt{\frac{}{7}}$

Calculate the square root of $\frac{8}{7}$ .
Since $\frac{8}{7}$ is not a perfect square, its square root will be an irrational number.
Therefore, the answer is option d, $\sqrt{\frac{8}{7}}$ .