Just an easy simplification

Number Theory Level 3

$\large 3 \sqrt{147} - \frac{7}{3} \sqrt{ \frac{1}{3} } + 7 \sqrt{ \frac{1}{3} } = \frac{a}{b} \sqrt{c}$

where $a$ and $b$ are positive co-primes and $c$ is not a perfect square .

Find $\large a + b + c$ .

This problem is a part of the sets - 1's & 2's & " N " for number theory .

The answer is 215.

1 solution

Félix de Montemar
Mar 18, 2015

$3\sqrt { 147 } -\frac { 7 }{ 3 } \sqrt { \frac { 1 }{ 3 } } +7\sqrt { \frac { 1 }{ 3 } } =3·7\sqrt { 3 } -\frac { 7 }{ 3 } ·\frac { \sqrt { 3 } }{ 3 } +7·\frac { \sqrt { 3 } }{ 3 } =\frac { \sqrt { 3 } }{ 9 } \left( 21·9-7+7·3 \right) =\frac { 203 }{ 9 } \sqrt { 3 } =\frac { a }{ b } \sqrt { c } \Rightarrow a+b+c=203+9+3=215$

Just an easy simplification

This problem is a part of the sets - 1's & 2's & " N " for number theory .

The answer is 215.

1 solution

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