QuestionFind an irrational number between 2 and 3. For example, consider $\sqrt{5}$ .

Studdy Solution

STEP 1

Assumptions1. An irrational number is a number that cannot be expressed as a simple fraction. . An irrational number has non-repeating, non-terminating decimal expansion.
3. We need to find an irrational number between and3.

STEP 2

One of the most common irrational numbers is the square root of a number that is not a perfect square. We can use this concept to find an irrational number between2 and.

STEP 3

We know that $2^2 =$ and $3^2 =9$ . So, if we find a number between and9, its square root will be an irrational number between2 and3.

STEP 4

Let's choose as it lies between4 and9. The square root of is an irrational number.
$rrational\, number = \sqrt{}$

STEP 5

Calculate the square root of5.
$rrational\, number = \sqrt{5} \approx2.23607$ The square root of5 is approximately2.23607, which is an irrational number between2 and3.

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QuestionFind an irrational number between 2 and 3. For example, consider $\sqrt{5}$ .

Studdy Solution

STEP 1

Assumptions1. An irrational number is a number that cannot be expressed as a simple fraction. . An irrational number has non-repeating, non-terminating decimal expansion.
3. We need to find an irrational number between and3.

STEP 2

One of the most common irrational numbers is the square root of a number that is not a perfect square. We can use this concept to find an irrational number between2 and.

STEP 3

We know that $2^2 =$ and $3^2 =9$ . So, if we find a number between and9, its square root will be an irrational number between2 and3.

STEP 4

Let's choose as it lies between4 and9. The square root of is an irrational number.
$rrational\, number = \sqrt{}$

STEP 5

Calculate the square root of5.
$rrational\, number = \sqrt{5} \approx2.23607$ The square root of5 is approximately2.23607, which is an irrational number between2 and3.

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QuestionFind an irrational number between 2 and 3. For example, consider 5 \sqrt{5} 5​.

Studdy Solution

STEP 1

Assumptions1. An irrational number is a number that cannot be expressed as a simple fraction. . An irrational number has non-repeating, non-terminating decimal expansion.3. We need to find an irrational number between and3.

STEP 2

One of the most common irrational numbers is the square root of a number that is not a perfect square. We can use this concept to find an irrational number between2 and.

STEP 3

We know that 22=2^2 =22= and 32=93^2 =932=9. So, if we find a number between and9, its square root will be an irrational number between2 and3.

STEP 4

Let's choose as it lies between4 and9. The square root of is an irrational number.rrational number=rrational\, number = \sqrt{}rrationalnumber=​

STEP 5

Calculate the square root of5.rrational number=5≈2.23607rrational\, number = \sqrt{5} \approx2.23607rrationalnumber=5​≈2.23607The square root of5 is approximately2.23607, which is an irrational number between2 and3.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind an irrational number between 2 and 3. For example, consider $\sqrt{5}$ .

Assumptions1. An irrational number is a number that cannot be expressed as a simple fraction. . An irrational number has non-repeating, non-terminating decimal expansion.
3. We need to find an irrational number between and3.

We know that $2^2 =$ and $3^2 =9$ . So, if we find a number between and9, its square root will be an irrational number between2 and3.

Let's choose as it lies between4 and9. The square root of is an irrational number.
$rrational\, number = \sqrt{}$

Calculate the square root of5.
$rrational\, number = \sqrt{5} \approx2.23607$ The square root of5 is approximately2.23607, which is an irrational number between2 and3.