Question

What is the following sum in simplest form? sqrt 8 + 3 sqrt2 + sqrt 32
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Answer 1

`√(8) +3 √(2)+ √(32) =\\\\ √(4*2)+3 √(2)+ √(16*2)=\\\\2 √(2)+3 √(2)+4 √(2)=\\\\ \boxed{9 √(2) }`

Answer 2

Answer:-
`√(8)+3 √(2)+ √(32)=9√(2)` in the simplest form.

Explanation:-

Given sum :-
`√(8)+3 √(2)+ √(32)`

To simplify, rewrite the numbers inside the root in the product of primes, we get

`\Rightarrow√(2*2*2)+3 √(2)+ √(2*2*2*2*2)\\\\\Rightarrow√(2^2*2)+3 √(2)+ √(4*4*2)\\\\\Rightarrow√(2^2)√(2)+3 √(2)+ √(4^2*2)\\\\\Rightarrow2√(2)+3√(2)+√(4^2)√(2)\\\\\Rightarrow2√(2)+3√(2)+4√(2)=9√(2)`

Thus
`√(8)+3 √(2)+ √(32)=9√(2)` in the simplest form.