Question 159235
this is a weird question to type out but basically I have to prove without using a calculator that (root)4 + (root that was above 4 continues)(root)7 [root that was above 4 ends]+ (root)4 - (root that was above 4 continues)(root)7 [root that was above 4 ends] = (root)14 
Plz help!!!
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Whenever you're asked to prove something, it might be true and it might not.  Let's find out.
I assume by "root" you mean square root.
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{{{sqrt((4)+sqrt(7)) + sqrt((4)-sqrt(7)) = sqrt(14)}}}
Square both sides
{{{4 + sqrt(7) + 4 - sqrt(7) + 2*sqrt((4)+sqrt(7))*sqrt((4)-sqrt(7)) = 14}}}
Collect terms
{{{8 + 2*sqrt((4)+sqrt(7))*sqrt((4)-sqrt(7)) = 14}}}
Multiply the 2 radicals
{{{8 + 2*sqrt(16 - 7) = 14}}}
{{{8 + 2*sqrt(9) = 14}}}
8 + 2*3 = 14
8 + 6 = 14
So it is true.