Question

3√8 /√2 rational or irrational​

Answer 1

which can be simplified even further to 4‾√2‾√
4
2
. Because 4‾√=2
4
=
2
, you can simplify this to 22‾√
2
2
. Now your expression can be written as 3⋅22√2√
3
⋅
2
2
2
. Cancelling the 2‾√
2
s in the numerator and denominator gives you 3⋅2
3
⋅
2
, or simply 6. Therefore, 38√2√
3
8
2
is equal to 6, which is not irrational, making 38√2√
3
8
2
not irrational.

Answer 2

Answer:

$\huge \bold \red{ irrational}$

$let \: us \: write \: 3\sqrt{8} \: as \: 2$

$\frac{3 \ \sqrt{2 \times 2 \times 2} }{ \sqrt{2} }$

$\bold \green{ = \frac{2}{ \sqrt{2} } }$

$\frac{ \sqrt{2} \times \sqrt{2} }{ \sqrt{2} }$

$= \sqrt{2}$

$\sqrt{2} \: is \: irrational$

$\huge \underline{ \: proved}$

$\huge \boxed{note : - }$

$\huge2 = \sqrt{2} \times \sqrt{2}$

$\huge3 \sqrt{8} = 3 \sqrt{2 \times 2 \times 2}$

$\huge\red{3 \sqrt{8} = {2}^{3}}$

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