Question

if X is the +ve real number then find the value of
$4 \sqrt{3 \sqrt{x {}^{2} } }$

Answer 1

Hlw mate

You have the right idea in squaring and then taking the square root.

Note that k=(4+23–√−−−−−−−√+4−23–√−−−−−−−√)2=4+23–√+2(4+23–√)(4−23–√)−−−−−−−−−−−−−−−−√+4−23–√k=(4+23+4−23)2=4+23+2(4+23)(4−23)+4−23

But this is just:

k=8+216−12−−−−−−√=12k=8+216−12=12

So

k−−√=23–√
Since (4+23–√)(4−23–√)=16−12=4(4+23)(4−23)=16−12=4, try squaring:

(4+23–√−−−−−−−√+4−23–√−−−−−−−√)2=(4+23–√)+(4−23–√)+2(4+23–√)(4−23–√)−−−−−−−−−−−−−−−−√=8+216−12−−−−−−√=12(4+23+4−23)2=(4+23)+(4−23)+2(4+23)(4−23)=8+216−12=12

Therefore, 4+23–√−−−−−−−√+4−23–√−−−−−−−√=23–√



Hope it helpful