M&N

Algebra Level 3

Given that:

( 125 + 5 + 4 2 5 − 3 ) 0.5 × 3 5 − 1 = m n { \left( \sqrt { 125 } +\frac { \sqrt { 5 } +4 }{ 2\sqrt { 5 } -3 } \right) }^{ 0.5 }\times \sqrt { 3\sqrt { 5 } -1 } =\quad m\sqrt { n }

Where m and n are integers, find the value of m + n m+n .


The answer is 24.

Gabriel Ong by Gabriel Ong , 21, Singapore

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Cai Kaian
May 12, 2014

( 5 5 + ( 5 + 4 ) ( 2 5 + 3 ) 11 ) ( 3 5 − 1 ) = ( 5 5 + 22 + 11 5 11 ) ( 3 5 − 1 ) = ( 6 5 + 2 ) ( 3 5 − 1 ) = 88 + 6 5 − 6 5 = 2 22 2 + 22 = 24 \sqrt { \left( 5\sqrt { 5 } +\frac { (\sqrt { 5 } +4)(2\sqrt { 5 } +3) }{ 11 } \right) (3\sqrt { 5 } -1) } \\ =\quad \sqrt { (5\sqrt { 5 } +\frac { 22+11\sqrt { 5 } }{ 11 } )(3\sqrt { 5 } -1) } \\ =\quad \sqrt { (6\sqrt { 5 } +2)(3\sqrt { 5 } -1) } \\ =\quad \sqrt { 88+6\sqrt { 5 } -6\sqrt { 5 } } \\ =\quad 2\sqrt { 22 } \\ 2\quad +\quad 22\quad =\quad 24

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice solution .

Chinmoyranjan Giri - 6 years, 12 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...