Question

1. n√ is called ______

2. In n√a , a is called _____.



II. Classify the following numbers as rational / irrational.



3. (√2 – 2)2



4. (2 + √2) (2-√2)



III. Find the x, y, z ……. Etc. represent rational / irrational.



5. x2 = 16.

6. y2 = 0.02.



IV. Rationalise the denomination of the following.

7. 1/3+√2.

8. 1/√7-√6.

​

Answer 1

Given : Question related to Surd , Rational & irrational number

To find : Identify Rational & irrartional number

Solution:

$\sqrt[n]{ }$   -  n is  order of Surd/Radical

$\sqrt[n]{a }$  - a is called Radicand  

√ -  Radical Symbol

(√2 – 2)2 = 2√2 - 4  - Irrational  Number

(2 + √2) (2-√2) = 2² - (√2)²

= 4 - 2

= 2  

= 2/1   Rational Number

x² = 16

=>  x = 4    

=> x - Rational Number  

y² = 0.02

=> y² = 2 * 0.01

=> y = 0.1√2

=> y -   Irrational  Number

1/(3+√2)

= (3 - √2) /(9 - 2)

=  (3 - √2) /7

1/(√7-√6)

= (√7+√6)/(7 - 6)

= √7+√6

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