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anonymous
 one year ago
simplify 5 square root of 7 + 12 square root of 6  10 square root of 7  5 square root of 6.
anonymous
 one year ago
simplify 5 square root of 7 + 12 square root of 6  10 square root of 7  5 square root of 6.

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0hint: we can factor out square root of 7 between the first and the third term, furthermore, we can factor out square root of 6 between the second and fourth term, so we can write the subsequent step: \[\Large \begin{gathered} 5\sqrt 7 + 12\sqrt 6  10\sqrt 7  5\sqrt 6 = \hfill \\ \hfill \\ = \sqrt 7 \left( {5  10} \right) + \sqrt 6 \left( {12  5} \right) = ... \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0honestly i dont know mate im really confused sorry... @Michele_Laino

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0following the rules of algebra of radicals, you can only sum similar radicals, namely radicals which have the same square roots as in your case

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0now, \[5\sqrt 7 ,\;  10\sqrt 7 \] are similar since they both have square root of 7, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i was trying to work it out and the answer i got was 5 square root of 7  7 quare root of 6

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I got this since 510= 5, we have: \[\sqrt 7 \left( {5  10} \right) =  5\sqrt 7 \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0furthermore 125=7, so we can write: \[\sqrt 6 \left( {12  5} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0oops.. \[\sqrt 6 \left( {12  5} \right) = 7\sqrt 6 \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and that will be 7 square root of 6  5 square root of 7 @Michele_Laino

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you so much can you help me with one more? @Michele_Laino

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0simplify square root of 5 (104 square root of 2) @Michele_Laino

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0we have to apply the distributive property of multiplication over addition, so we can write this: \[\Large \sqrt 5 \left( {10  4\sqrt 2 } \right) = 10\sqrt 5  4\sqrt 5 \sqrt 2 \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Michele_Laino is that the answer to the question?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0no, we have to write another step

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhhhhh okay well as i simplify it i got 5 square root of 2  4 square root of 10 @Michele_Laino

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0more precisely we can write this: \[\sqrt 5 \sqrt 2 = \sqrt {5 \times 2} = \sqrt {10} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea thats what i got @Michele_Laino

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0so we get: \[\sqrt 5 \left( {10  4\sqrt 2 } \right) = 10\sqrt 5  4\sqrt {10} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0furthermore we can note that: \[10 = \sqrt {10} \sqrt {10} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0so we can write: \[\sqrt 5 \left( {10  4\sqrt 2 } \right) = 10\sqrt 5  4\sqrt {10} = \sqrt {10} \sqrt {10} \sqrt 5  4\sqrt {10} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0finally, I factor out sqrt(10) and I get: \[\begin{gathered} \sqrt 5 \left( {10  4\sqrt 2 } \right) = 10\sqrt 5  4\sqrt {10} = \sqrt {10} \sqrt {10} \sqrt 5  4\sqrt {10} \hfill \\ = \sqrt {10} \left( {\sqrt {10} \sqrt 5  4} \right) \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its not too difficult just follow what the question is trying to tell you.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0recalling taht: \[\sqrt {10} \sqrt 5 = \sqrt {10 \times 5} = \sqrt {50} \] we have: \[\begin{gathered} \sqrt 5 \left( {10  4\sqrt 2 } \right) = 10\sqrt 5  4\sqrt {10} = \sqrt {10} \sqrt {10} \sqrt 5  4\sqrt {10} \hfill \\ \hfill \\ = \sqrt {10} \left( {\sqrt {10} \sqrt 5  4} \right) = \sqrt {10} \left( {\sqrt {50}  4} \right) \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0there is another way to simplify your radical

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I start from the initial expression: \[\Large \sqrt 5 \left( {10  4\sqrt 2 } \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0and I factor out a 2 inside the parentheses: \[\Large 10  4\sqrt 2 = 2\left( {5  2\sqrt 2 } \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0so I can write: \[\Large \sqrt 5 \left( {10  4\sqrt 2 } \right) = \sqrt 5 \cdot 2\left( {5  2\sqrt 2 } \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0and we have finished

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0now you can choose the method which do you prefer
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