Identify square root of 11 as either rational or irrational, and approximate to the tenths place. (4 points)
Rational: square root of 11 ≈ 3.3
Rational: square root of 11 ≈ 3.4
Irrational: square root of 11 ≈ 3.3
Irrational: square root of 11 ≈ 3.4
Irrational: square root of 11 ≈ 3.3
The square root of 11 is an irrational number. It cannot be expressed as a fraction, and its decimal approximation is approximately 3.3 to the tenths place.
To determine whether the square root of 11 is rational or irrational, we need to approximate it to the tenths place.
First, we need to understand the definition of rational and irrational numbers. A rational number is a number that can be expressed as a fraction of two integers, whereas an irrational number cannot be expressed as a fraction and has an infinite, non-repeating decimal representation.
To approximate the square root of 11 to the tenths place, we need to find a number whose square is close to 11. We can start by trying some values:
- √9 = 3, which is less than 11
- √16 = 4, which is greater than 11
Since 11 is between the squares of 3 and 4, we can conclude that the square root of 11 is between 3 and 4.
Now, let's approximate it to the tenths place. We can make an educated guess and try √11 ≈ 3.3 and √11 ≈ 3.4.
To check whether these approximations are correct, we can square them and see if they equal 11:
- (3.3)^2 ≈ 10.89 (approximately),
- (3.4)^2 ≈ 11.56 (approximately).
Since neither of these squared values exactly equals 11, we can conclude that neither approximation is correct. Therefore, the square root of 11 is irrational and cannot be expressed as a fraction.