Question

Find three irrational number between 6 and 7

Answer 1

Answer:

$Three \: irrational\: numbers\\between \:6 \:and \:7\: are \:\sqrt{6\sqrt{42}},\\\sqrt{42}\\and\:\sqrt{7\sqrt{42}}$

Or,

Three irrational numbers between 6 and 7 are

i )6.2020020002...

ii) 6.5010010001....

iii)6.9010010001....

Step-by-step explanation:

$If \:a \:and \: b \: are\\two\: positive\: rational \\ numbers\:such \:that \:ab\\is \: not \: a \: perfect \: square\\of\:a\: rational\:number ,\\then \: \sqrt{ab}\:is \:an \\irrational \: number\:lying \: between \:a \:and \: b$

$Here , a = 6 \: and \: b = 7\\</p><p>i) An \: irrational\: number \\between\:6 \: and \:7 = \sqrt{6\times 7}\\=\sqrt{42}$

$ii)Here , a = 6 \: and \: b = \sqrt{42}\\</p><p>An \: irrational\: number \\between\:6 \: and \:\sqrt{42} = \sqrt{6\times \sqrt{42}}\\=\sqrt{6\sqrt{42}}$

$Here, \: a = \sqrt{42}\: and \: b = 7\\</p><p> An \: irrational\: number \\between\:\sqrt{42} \: and \:7\ = \sqrt{\sqrt{42}\times 7}\\=\sqrt{7\sqrt{42}}$

Therefore,.

$Three \: irrational\: numbers\\between \:6 \:and \: 7\: are \: \sqrt{6\sqrt{42}},\sqrt{42}\\and\:\sqrt{7\sqrt{42}}$

Or,

Three irrational numbers between 6 and 7 are

i )6.2020020002...

ii) 6.5010010001....

iii)6.9010010001....

•••♪

Answer 2

Answer:

answer is 12>13>14>……hence 13 is irrational number.

Step-by-step explanation:

they asked to find one irrational so take 2(more than one).

so,6×2 , 7×2

that is 12and14

so,12>13>14

plsssss mark as brainlist