Question

Evaluate :√(12-2√35)

Answer 1

Answer:

Let's take the square root of (12-2√35) be √x-√y So we know that

${( \sqrt{x} - \sqrt{y} )}^{2} = 12 - 2 \sqrt{35} = >$

$x + y - 2 \sqrt{xy} = 12 - 2 \sqrt{35} = >$

$x + y = 12 \: and \: xy = 35 = >$

$y = \frac{35}{x} = > x + \frac{35}{x} = 12 = >$

${x}^{2} - 12x + 35 = 0 = > {x}^{2} - 7x - 5x$

$+ 35 = 0 = > x(x - 7) - 5(x - 7) =$

$0 = > (x - 5)(x - 7) = 0 = >$

$x = 5 \: or \: 7 = > \sqrt{x} = \sqrt{7}$

So x+y =12 => y=12-7=5 =>√y =√5 Hence the square root of 12-2√35 =>

(√7-√5). Hope it helps you.