Question

$\:$
plz give answers


no copied answers or irrelevant answers otherwise I'd will report ​

Answer 1

$\huge \pink{ \boxed{ \sf{ \green{Answer:-}}}}$

State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.

Solution:

True

Irrational Numbers – A number is said to be irrational, if it cannot be written in the p/q, where p and q are integers and q ≠ 0.

i.e., Irrational numbers = ‎π, e, √3, 5+√2, 6.23146…. , 0.101001001000….

Real numbers – The collection of both rational and irrational numbers are known as real numbers.

i.e., Real numbers = √2, √5, 0.102…

Every irrational number is a real number, however, every real numbers are not irrational numbers.

(ii) Every point on the number line is of the form √m where m is a natural number.

Solution:

False

The statement is false since as per the rule, a negative number cannot be expressed as square roots.

E.g., √9 =3 is a natural number.

But √2 = 1.414 is not a natural number.

Similarly, we know that there are negative numbers on the number line but when we take the root of a negative number it becomes a complex number and not a natural number.

E.g., √-7 = 7i, where i = √-1

The statement that every point on the number line is of the form √m, where m is a natural number is false.

(iii) Every real number is an irrational number.

Solution:

False

The statement is false, the real numbers include both irrational and rational numbers. Therefore, every real number cannot be an irrational number.

Real numbers – The collection of both rational and irrational numbers are known as real numbers.

i.e., Real numbers = √2, √5, 0.102…

Irrational Numbers – A number is said to be irrational, if it cannot be written in the p/q, where p and q are integers and q ≠ 0.

i.e., Irrational numbers = π, e, √3, 5+√2, 6.23146…. , 0.101001001000….

Every irrational number is a real number, however, every real number is not irrational.

• HOPE IT HELPS YOU...
• MARK AS BRAINLIEST...
• FOLLOW ME...
• THANK MY ANSWERS...

Answer 2

$\huge\mathcal\color{green}Question.1$

(i) TrueReason: Real numbers are any number which can we think about. Thus, every irrational number is a real number.

(ii) False

Reason: A number line may have negative or positive number. Since, no negative can be the square root of a natural number, thus every point on the number line cannot be in the form of √m, where m is a natural number.

(iii) False

Reason: All numbers are real number and non terminating numbers are irrational number. For example 2, 3, 4, etc. are some example of real numbers and these are not irrational.

$\huge\mathcal\color{green}Question.2$

Answer: No. Square roots of all positive integers are not irrational. Example 4, 9, 16, etc. are positive integers and their square roots are 2, 9 and 4 which are rational numbers.

$\huge\mathcal\color{green}Question.3$

Steps to show √5 on a number line.

Step: 1 – Draw a number line mm’

Step: 2 – Take OA equal to one inch, i.e. one unit.

Step: 3 – Draw a perpendicular AB equal to one inch (1 inch) on point A.

Step: 4 – Join OB. This OB will be equal to √2

Step: 5 – Draw a line BC perpendicular to OB on point B equal to OA i.e. one inch.

Step: 6 – Join OC. This OC will be equal to √3

Step: 7 – Draw a line CD equal to OA and perpendicular to OC.

Step: 8 – Join OD. This will be √4 i.e. equal to 2.

Step: 9 – Draw ED equal to 1 inch and perpendicular to OD.

Step: 10 – Join OE. This will be equal to √5

Step: 11 – Cut a line segment OF equal to OE on number line. This line segment OF will be equal to √5

See how, OE is equal to √5

Here, OD = 2, DE = 1 and angle ODE = 90º

Thus, according to Pythagoras theorem.