Exercise 1

Classify the following numbers:

\frac {\pi}{2}

\sqrt{36}

2.25111...

\sqrt{-5}

\frac{75}{-5}

Exercise 2

Represent the following number in the real line:

\sqrt{17}

Exercise 3

Represent the numbers that verify the following relations in the real line:

|X| < 1

|x| \leq 1

|x| > 1

|x| \geq 1

Exercise 4

Calculate the values of the following powers:

16 ^ {\frac{3}{2}}

8 ^ {\frac{2}{3}}

81 ^ {0.75}

Exercise 5

Represent the following number in the real line:

\sqrt{13}

 

Exercise 6

Represent the following relations in the real line using real numbers:

|X - 2| < 1

|x - 2| \leq 1

|x - 2| >1

|x - 2| \geq 1

 

Solution of exercise 1

Classify the following numbers:

\frac {\pi}{2} \in R

\sqrt{36} \in N

2.25111... \in Q

\sqrt{-5}\notin R

\frac{75}{-5} \in Z

 

Solution of exercise 2

Represent the following number in the real line:

\sqrt{17}

\sqrt {17} = 4^2 + 1^2

 

Solution of exercise 2

 

Solution of exercise 3

Represent the numbers that verify the following relations in the real line:

|x| < 1          |x| \leq 1         |x| > 1           |x| \geq 1

|x| < 1           -1 < x < 1             x \in (-1, 1)

Solution of exercise 3

|x| \leq 1          -1 \leq x \leq 1           x \in [-1, 1]

Solution of exercise 3

|x| > 1          -1 > x > 1           x \in (-\infty, -1) U (1, +\infty)

=

Solution of exercise 3

|x| \geq 1             -1 \geq x \geq 1            x \in (-\infty, -1] U [1, +\infty)

Solution of exercise 3

 

Solution of exercise 4

Calculate the values of the following powers:

16 ^ {\frac{3}{2}} = \sqrt {16^3} = \sqrt{(2^4)^3} = \sqrt {2 ^{12}} = 2^6 = 64

8 ^ {\frac{2}{3}} = \sqrt[3] {8^2} = \sqrt[3] {(2^3)^2} = \sqrt[3] {2^6} = 2^2 = 4

81 ^ {0.75} = 81 ^ {\frac{75}{100}} = 82^ {\frac{3}{4}} = \sqrt [4] {(3^4)^3} = \sqrt [4] {3^{12}} = 3^3 = 27

 

Solution of exercise 5

Represent the following number in the real line:

\sqrt{13}

\sqrt{13} = 3^2 + 2^2

Exercise 5 - Solution

 

Solution of exercise 6

Represent the following relations in the real line using real numbers:

|x - 2| < 1           |x - 2| \leq 1             |x - 2| > 1             |x - 2| \geq 1

|x - 2| < 1             -1 < x - 2 < 1              1 < x < 3

X \in (1, 3)

Solution of exercise 6

|x - 1| \leq 1            -1 \leq x - 2 \leq 1            1 \leq x \leq 3

x \in [1, 3]

Solution of exercise 6

|x - 2| > 1          -1 > x - 2 > 1            1 > x > 3

x \in (-\infty, 1) U (3, +\infty)

Solution of exercise 6

|x - 2| \geq 1              -1 \geq x - 2 \geq 1              1 \geq x \geq 3

x \in (-\infty, 1] U [3, + \infty)

Solution of exercise 6

 

Need a Maths teacher?

Did you like the article?

1 Star2 Stars3 Stars4 Stars5 Stars 5.00/5 - 1 vote(s)
Loading...

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.