14. (2 + √5) (2 + √5) expression is:-
(a) A rational number
(b) A whole number
(c) An irrational number
(d A natural number
Answers
Answer:
(c) An irrational number
Step-by-step explanation:
Given,
(2+√5)(2+√5)
To know whether it's a rational, a whole, an irrational or a natural number,
First of all,
Let's evaluate it's value.
Therefore, we will get,
= (2+√5)(2+√5)
= (2+√5)^2
= (2)^2 + 2(2)(√5) + (√5)^2
= 4 + 4√5 + 5
= 9 + 4√5
Now, in this value,
9 is a natural, a whole and a rational number.
4√5 is an irrational number.
Overall, we have,
(9+4√5) is an irrational number.
Hence, the correct answer is (c) an irrational number
✯✯ QUESTION ✯✯
(2 + √5) (2 + √5) expression is:-
(a) A rational number
(b) A whole number
(c) An irrational number
(d A natural number
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✰✰ ANSWER ✰✰
➥Firstly we will evaluate (2+√5) (2+√5)...
➥Using Identity : -
➥Putting Values : -
➜Here , 9 is a rational ,natural and whole number but 4√5 is irrational number...So,
So,It is an irrational number...
☛Option c) is the correct....
_______________________
✔Definitions : -
★Rational Number : -
A number that can be written in the form of p/q where p and q are integers and q≠0 are called as Rational Numbers...
For Eg:.4/10,67/87....etc...
★Irrational Number : -
A number that cannot be written in the form of p/q where p and q are integers and q≠0 are called as Irrational Numbers...
For Eg:. 0.121212...,√3....etc...