Question

Describe the following nimbers:√8,-√40,√50,and -√90 are the numbers rational or irrational?​

Answer 1

$\underline {\pink{ Rational \: number : }}$

$A\: number \:which\: can\: be\: written\: in\\ the\: form \: of \: \frac{p}{q} , where \: 'p' \:and \: 'q'\\are \: integers \: and \: q \neq 0 \: is \: called \: a \\Rational \: number$

Examples:

$\frac{2}{7} , \frac{7}{7} , \frac{-2}{9} , 0.23 ,0.\bar{5}, \ldots$

$\underline {\blue{ Irrational \: number : }}$

A number which cannot be expressed as a terminating decimal or a repeating decimal is called an Irrational number .

Examples:

$1. 1.4141251\ldots \: 2) 0.010010001\ldots ,\\3) \sqrt{2} , \sqrt{7} , etc.,$

$Here, 1 ) \sqrt{8} \\= \sqrt{ 2\times 2 \times 2 } \\= 2 \sqrt{2} \: \green { ( Irrational \:number )}$

$2) - \sqrt{40} \\= - \sqrt{ 2 \times 2 \times 2 \times 5 } \\= - 2 \sqrt{ 2 \times 5 } \\= - 2 \sqrt{10} \: \green { ( Irrational \:number )}$

$3) \sqrt{50 } \\= \sqrt{ 2 \times 5 \times 5 } \\= 5\sqrt{2} \: \green { ( Irrational \:number )}$

$4 ) - \sqrt{90} \\= - \sqrt{ 2 \times 3 \times \times 3 \times 5 } \\= - 3 \sqrt{ 2 \times 5 } \\= - 3 \sqrt{10} \: \green { ( Irrational \:number )}$

•••♪