Question

is (2+√3) (2-√3) a rational or irrational.

who explains with full process I will mark them as brainlist​

Answer 1

${\large{\pmb{\sf{\underline{RequirEd \: solution...}}}}}$

⋆ Understanding the question: This question says that we have to tell that the given expression is rational or irrational. The given expression is (2+√3) (2-√3)

⋆ Using concept: To solve this question we have to use an identity that is mentioned below:

${\small{\underline{\boxed{\sf{Suitable \: identity \longrightarrow (a+b) (a-b) = a^2 - b^2}}}}}$

⋆ Now let's solve this question!

~ According to the identity here

${\sf{:\implies (a+b) (a-b) = a^2 - b^2}}$

${\sf{:\implies a \: is \: 2 \: and \: b \: is \: \sqrt{3}}}$

~ Now let's put values and solve

${\sf{:\implies (2)^{2} - (\sqrt{3})^{2}}}$

~ (Don't forget) Square and square root cancel each other.

${\sf{:\implies 4 - 3}}$

${\sf{:\implies 1 \:is \: required \: solution}}$

As we get 1 as required solution henceforth, the expression that is (2+√3) (2-√3) a rational number!

${\large{\pmb{\sf{\underline{Additional \: KnowlEdge...}}}}}$

Rational number: Rational number are those numbers which can be written in the form of ${\sf{\dfrac{p}{q}}}$ where q ≠ 0 i.e., q is not equal to zero. Some example of rational number are ${\sf{\dfrac{23}{9} \: , \dfrac{777}{44432}}}$

Irrational number: Irrational number are the inverse of rational numbers. These numbers can't be written in the form of ${\sf{\dfrac{p}{q}}}$ The bestest example for irrational numbes are ${\sf{\pi}}$ and ${\sf{\sqrt{}}}$