Understanding Root 3 and Root 5

Oct 13, 2025 by recoveryshake.com 101 views

Which of the Following is a Rational Number Between Root 3 and Root 5?

In mathematics, rational numbers are those that can be expressed as the ratio of two integers, i.e., in the form of p/q where p and q are integers and q is not equal to zero. Rational numbers can be expressed in decimal form, but they may or may not have a terminating or repeating decimal expansion. In this article, we will discuss which of the given options is a rational number between root 3 and root 5.

Understanding Root 3 and Root 5

Root 3 and root 5 are two irrational numbers that are obtained by taking the square root of 3 and 5 respectively. These numbers are irrational because they cannot be expressed as a finite decimal or fraction. Root 3 is approximately equal to 1.73205080757, while root 5 is approximately equal to 2.2360679775.

Rational Numbers Between Root 3 and Root 5

To find a rational number between root 3 and root 5, we need to look for a number that can be expressed as a fraction in its simplest form. Let's analyze the given options:

Option A: 1.414238795..

This number is approximately equal to the square root of 2, which is an irrational number. However, it is not between root 3 and root 5.

Option B: 2.32666.....

This number is not a rational number because it has a repeating decimal expansion.

Option C: 3.14.....

This number is approximately equal to the square root of 10, which is an irrational number. However, it is not between root 3 and root 5.

Option D: 1.857142

This number can be expressed as a fraction in its simplest form, i.e., 24/13. Therefore, it is a rational number.

In conclusion, the correct answer is option D: 1.857142. This number is a rational number because it can be expressed as a fraction in its simplest form, i.e., 24/13. It is also between root 3 and root 5.

Rational numbers can be expressed as the ratio of two integers.
Rational numbers can be expressed in decimal form, but they may or may not have a terminating or repeating decimal expansion.
Root 3 and root 5 are irrational numbers that are obtained by taking the square root of 3 and 5 respectively.
To find a rational number between root 3 and root 5, we need to look for a number that can be expressed as a fraction in its simplest form.

What is a rational number? A rational number is a number that can be expressed as the ratio of two integers.
What is the difference between a rational number and an irrational number? A rational number can be expressed as a fraction in its simplest form, while an irrational number cannot be expressed as a fraction in its simplest form.
How do we find a rational number between root 3 and root 5? We need to look for a number that can be expressed as a fraction in its simplest form.

CBSE Board Syllabus for Mathematics
Khan Academy: Rational Numbers
Math Open Reference: Rational Numbers
Frequently Asked Questions: Rational Numbers Between Root 3 and Root 5

A rational number is a number that can be expressed as the ratio of two integers, i.e., in the form of p/q where p and q are integers and q is not equal to zero.

A rational number can be expressed as a fraction in its simplest form, while an irrational number cannot be expressed as a fraction in its simplest form. Irrational numbers have decimal expansions that go on indefinitely without repeating.

To find a rational number between root 3 and root 5, we need to look for a number that can be expressed as a fraction in its simplest form. We can start by finding the decimal expansions of root 3 and root 5, and then look for a number that falls between these two values.

Yes, we can use a calculator to find a rational number between root 3 and root 5. We can enter the values of root 3 and root 5 into the calculator, and then use the calculator's built-in functions to find a rational number between these two values.

We can use various methods to determine if a number is a rational number or an irrational number. One way is to try to express the number as a fraction in its simplest form. If we can do this, then the number is a rational number. If we cannot do this, then the number is an irrational number.

No, we cannot have a rational number that is equal to an irrational number. By definition, a rational number can be expressed as a fraction in its simplest form, while an irrational number cannot be expressed as a fraction in its simplest form.

Yes, we can have a rational number that is between two irrational numbers. For example, we can have a rational number that is between root 3 and root 5.

To find the decimal expansion of a rational number, we can use the following steps:

Express the rational number as a fraction in its simplest form.
Divide the numerator by the denominator to get the decimal expansion.

Yes, we can have a rational number that has a repeating decimal expansion. For example, the rational number 1/3 has a repeating decimal expansion of 0.33333...

Yes, we can have a rational number that has a terminating decimal expansion. For example, the rational number 1/2 has a terminating decimal expansion of 0.5.

In conclusion, rational numbers are numbers that can be expressed as the ratio of two integers. We can use various methods to determine if a number is a rational number or an irrational number. We can also use calculators to find rational numbers between two irrational numbers.