Math, asked by neelamgarg091, 11 months ago

14. (2 + √5) (2 + √5) expression is:-
(a) A rational number
(b) A whole number
(c) An irrational number
(d A natural number​​

Answers

Answered by Anonymous
2

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

Answered by sethrollins13
3

✯✯ QUESTION ✯✯

(2 + √5) (2 + √5) expression is:-

(a) A rational number

(b) A whole number

(c) An irrational number

(d A natural number

━━━━━━━━━━━━━━━━━━━━

✰✰ ANSWER ✰✰

Firstly we will evaluate (2+5) (2+5)...

\longmapsto\tt{(2+\sqrt{5)}(2+\sqrt{5)}}

\longmapsto\tt{{2+\sqrt{5}}^{2}}

Using Identity : -

\longmapsto\tt{{(a+b)}^{2}={a}^{2}+2ab+{b}^{2}}

Putting Values : -

\longmapsto\tt{{(2)}^{2}+2(2)\sqrt{(5)}+\sqrt{{(5)}}^{2}}

\longmapsto\tt{4+4\sqrt{(5)}+5}

\longmapsto\tt{4+4\sqrt{(5)}+5}

\longmapsto\tt{9+4\sqrt{5}}

Here , 9 is a rational ,natural and whole number but 45 is irrational number...So,

So,It is an irrational number...

Option c) is the correct....

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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...

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