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45 votes
45 votes
Identify as either
√(2)rational or irrational and approximate to the tenths place.

User Felixbade
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1 Answer

12 votes
12 votes

You have the following real number:

√2

In order to determine if the previous number is rational or irrational, remember that an irrational number is the number that in its decimal form has infinite digits, and it is not possible to identy a periodicity. Rational number are all number that can be expressed as a fraction, in wich it decimal form is finite or infinite but with a certain periodicty.

You evaluate the square root of 2 in a calculator and obtain:

√2 = 1.414213562...

In this case you can observe that √2 is a number with infinite digits without any periodicity. Then √2 is an irrational number.

The approximation to the tenths place of √2 is:

√2 ≈ 1.41

the tenth place is 1 because the number right side of this 1 is 4, then, the number 1 stays the same

User Batman Rises
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