Question

Какое из данных чисел √8,1 √810 √8100 является рациональным ???

Answer 1

√8100=90 оно и является рациональным числом

Answer 2

Rationality of Square Roots

To determine which of the given numbers √8.1, √810, and √8100 is rational, we need to understand the concept of rational numbers and how they relate to square roots.

A rational number is a number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In other words, a rational number can be written in the form a/b, where a and b are integers and b is not zero.

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 * 3 = 9.

Now, let's examine each of the given numbers to determine if their square roots are rational.

1. √8.1: The square root of 8.1 is approximately 2.8460498941515415. Since this number is not an exact integer or a fraction, it is an irrational number. Therefore, √8.1 is not rational.

2. √810: The square root of 810 is exactly 30. Since 30 is an integer, it can be expressed as the fraction 30/1. Therefore, √810 is rational.

3. √8100: The square root of 8100 is exactly 90. Since 90 is an integer, it can be expressed as the fraction 90/1. Therefore, √8100 is rational.

Based on the analysis above, we can conclude that √810 and √8100 are rational numbers, while √8.1 is an irrational number.