Simple complex

Algebra Level 4

$\sqrt{ 7 - 30\sqrt{-2}} = ( \pm \frac{ a \pm b\sqrt{c} i }{d})$

a, b, c, d are positive integers

a and d are coprime.

c is not divisible by the square of any prime.

Find a + b + c + d .

1 solution

Shohag Hossen
Jul 6, 2015

At first,

= 7 - 30*sqrt (-2) [ here sqrt, means square root ]

= 7 - 30*sqrt (2) * i [ i = sqrt ( -1 ) , from complex number ]

= ( 5 )^2 - 2.5.3.sqrt( 2 ) i + ( 3 * sqrt( 2 ) i )^2 [ rule's of (a - b)^2 ]

= ( 5 - 3 * sqrt( 2 ) * i )^2

So, sqrt ( 7 - 30*sqrt ( -2 ) ) = +,- ( 5 - 3 . sqrt( -2 ) ) [ We compared it by RHS ]

So, here , a = 5, b = -3, c = -2 , and d=1;

So, a + b + c + d = 5 - 3 - 2 +1 = 1

answer = 1.

On the $3^{rd}$ step , you should write $253$ as $2 \cdot 5 \cdot 3$ or else anyone can get confused.

Please look over your solution and use Latex .

Thanks :-)

Akshat Sharda - 5 years, 10 months ago

oh!! yes . This is really mistake. Thank you. I will edit it.

Shohag Hossen - 5 years, 9 months ago