9. Classify the following as rational or irrational
(a) (√3+√2)(√3-√2)
Share
9. Classify the following as rational or irrational
(a) (√3+√2)(√3-√2)
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
Given: (√3 + √2)(√3 - √2)
To find: Classify whether the given expression is rational or irrational.
⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀
Understanding the question: There is a expression given to us and we've to classify it as rational or irrational, We'll use a suitable law of exponent and simplify it !
▪︎ As a, b can be classified, we can use any law of exponent according to the question.
✇ Now, By using the law of exponent given below. Then let's find out whether the given question is rational or irrational —
⠀⠀⠀⠀
[tex]\star\:{\underline{\boxed{\pmb{\sf{\Big( \sqrt{a} - \sqrt{b} \Big) \Big( \sqrt{a} + \sqrt{b} \Big) = \Big( \sqrt{a} \Big)^2 - \Big( \sqrt{b} \Big)^2}}}}}[/tex]
⠀⠀⠀⠀
[tex]\begin{gathered}\twoheadrightarrow \sf \big(\sqrt{3} - \sqrt{2} \Big) \Big( \sqrt{3} + \sqrt{2} \Big) \sf \\\\\\\twoheadrightarrow\sf \Big( \sqrt{a} - \sqrt{b} \Big) \Big( \sqrt{a} + \sqrt{b} \Big) = \Big( \sqrt{a} \Big)^2 - \Big( \sqrt{b} \Big)^2\\\\\\\twoheadrightarrow\sf \big(\sqrt{3} - \sqrt{2} \Big) \Big( \sqrt{3} + \sqrt{2} \Big) = \Big( \sqrt{3} \Big)^2 - \Big( \sqrt{2} \Big)^2\\\\\\\twoheadrightarrow\sf 3 - 2\\\\\\\dashrightarrow\underline{\boxed{\pmb{\frak{\pink{\dfrac{1}{1}}}}}}\;\bigstar\end{gathered} [/tex]
⠀⠀⠀⠀⠀
Therefore,
⠀⠀⠀⠀
[tex]\therefore{\underline{\pmb {\sf{Hence, (\sqrt{3} - \sqrt{2}) (\sqrt{3} + \sqrt{2} ) \: is \: a \: rational \: number, Respectively.}}}}[/tex]
⠀⠀⠀⠀
⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀
⠀⠀⠀⠀⠀✇ [tex]\underline{ \pmb{ \frak{ \red{Additional \: information...}}}}[/tex]
⠀⠀⠀
⠀⠀⠀
⠀⠀⠀
⠀⠀⠀
⠀⠀⠀
⠀⠀⠀
⠀⠀⠀