**Telangana SCERT Solution Class IX (9) Math Chapter 1 Real Numbers Exercise 1.2**

**(1.) Classify the following numbers as rational or irrational.**

**(i) √27**

Solution: √27 = √9 x √3

= 3√3

Therefore, √27 is an irrational number.

**(ii) √441**

Solution: √441 = √3 x √147

= √3 x √3 x √49

= √3 x √3 x √7 x √7

= 3 x 7

= 21

Therefore √441 is a rational number.

**(iii) 30.232342345…**

Solution: It is an irrational number because the above given number is a non-terminating decimal number and non-recurring decimal number.

**(iv) 7.484848… **

Solution: the above mentioned number is rational number because it is a non terminating decimal number but it can be expressed in fractions. since it is a recurring decimal.

**(v) 11.2132435465**

Solution: The above mentioned number is a non-terminating and non-recurring decimal number hence it is an irrational number.

**(vi) 0.3030030003…**

Solution: The above given number is non-terminating and non-recurring hence it is an irrational number.

**(2.) Give four examples for rational and irrational numbers?**

Solution: For example of rational number are,

1, 2, 2/3, 4/5

Four example of an irrational number are,

√2, √3, √5, π (pi).

**(4.) Find two irrational numbers between 0.7 and 0.77**

Solution: Two irrational numbers between 0.7 and 0.77 are

i) 0.745689…,

ii) 0.732145

[Any random non-recurring and non terminating number between the given number can be treated as irrational numbers].

**(5.) Find the value of √5 upto 3 decimal places**

Solution: Using long division method to find out the value of √5

Step 1: You take the values to be calculated and put 3 pair of zero in it after a decimal point.

Step 2: Now take a number lower than the given number and multiply it with itself. so that the result is also lower then the given number in this case it is 2.

Step 3: Put the number in quotient and dividend and subtracts the result from the divisor.

Step 4: Put the pair of zeros beside the remainder, and add the quotient with the dividend and put it on the next dividend in this case its 2 + 2 = 4.

Step 5: Now, calculate and chose a number that when put beside the dividend and multiplied with itself gives a number that is lower than the total remainder or the new devisor in this case its 42 x 2 = 84 < 100

Step 6: Follow the above steps until you get upto.

**(8.) Find atleast two irrational numbers between 2 and 3.**

Solution: Given,

a = 2, b = 3

To find irrational number between 2 and 3 √ab should not be a perfect square.

∵ ab = 2 x 3 = 6 [Not a perfect square]

∴ an irrational number between 2 and 3 is √6.

Another method ->

2^{2} = 4 and 3^{2} = 9

so the numbers between 4 and 9 are not perfect squares hence the square root of those numbers are irrational and they lay between 2 and 3.

∴ √5, √7 are also two irrational numbers between 2 and 3.

**(9.) State whether the following statements are true or false. Justify your answers.**

**(i) Every irrational number is a real number.**

Ans. True.

**(ii) Every rational number is a real number.**

Ans. True.

**(iii) Every real number need not be a rational number**

Ans. True.

**(iv) √n is not irrational if n is a perfect square.**

Ans. True.

**(v) √n is irrational if n is not a perfect square.**

Ans. True.

**(vi) All real numbers are irrational.**

Ans. False.

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