Answer. Since, 4 can be written as 4/1, 4 is a rational number. Therefore, **√8 into √2 is rational**.

Expert-Verified Answer

8-√2 is an Irrational number.

Hence, the square root of 8 is an irrational number.

We can say that √2 is not a rational number. √2 is an irrational number.

√2√2 is irrational.

∴ The given number is an Irrational number.

2/root 3 is irrational.

Therefore, 1√2 cannot be rational. Hence, it is irrational.

Specifically, the Greeks discovered that the diagonal of a square whose sides are 1 unit long has a diagonal whose length cannot be rational. By the Pythagorean Theorem, the length of the diagonal equals the square root of 2. So the square root of 2 is irrational!

3 is a rational number and √3 is an irrational number.

Table of Content. Irrational numbers are non-terminating and non-repeating numbers, as we know. Thus, we can check each of the given options. Therefore, option (B) i.e., 3√8 is the correct answer.

Rational Numbers

The number 8 is a rational number because it can be written as the fraction 8/1.

Also, the root of 9 is a rational number, because we can represent √9 = ±3 in the form P/Q, such as 3/1.

Hence, √2*√8 is a rational number.

We need to express 8 as the product of its prime factors i.e. 8 = 2 × 2 × 2. Therefore, √8 = √2 × 2 × 2 = 2 √2. Thus, the square root of 8 in the lowest radical form is 2 √2.

(ii) As we know that the subtraction of a rational and irrational number is irrational then √7 – 2 is irrational.

Sal proves that the square root of 2 is an irrational number, i.e. it cannot be given as the ratio of two integers.

√2 is irrational. Now we know that these irrational numbers do exist, and we even have one example: √2. It turns out that most other roots are also irrational.

A rational number is defined as a number that can be expressed in the form of a division of two integers, i.e. p/q, where q is not equal to 0. √3 = 1.7320508075688772... and it keeps extending. Since it does not terminate or repeat after the decimal point, √3 is an irrational number.

Assume that the total of √3 +√ 5 is a rational number. Here a and b are integers, then (a^{2}-8b^{2})/2b is a rational number. Then √15 is also a rational number. However, this is incompatible because 15 is an irrational number.

∵2√5 is an irrational number.

Therefore, 7√5 is an irrational number.

Hence, 0.666666.. is a rational number.

Irrational numbers are those real numbers that cannot be represented in the form of p/q. In other words, those real numbers that are not rational numbers are known as irrational numbers. √2 + √3 is irrational.

It is a rational number. Was this answer helpful?