Question

Помогите решить 535,536 пожалуйста

Answer 1

535.
$frac{a}{3 sqrt{5} } = frac{a sqrt{5} }{3 sqrt{5} sqrt{5} } = frac{a sqrt{5} }{3( sqrt{5})^2} = frac{a sqrt{5} }{3*5} = frac{a sqrt{5} }{15} \ \ frac{4b}{5 sqrt{c} } = frac{4b* sqrt{c} }{5*( sqrt{c} )^2} = frac{4b sqrt{c} }{5c} \ \ frac{6}{ sqrt{a+b}} = frac{6 sqrt{a+b} }{( sqrt{a+b} )^2} = frac{6 sqrt{a+b} }{a+b} \ \ frac{4}{ sqrt{x-y} } = frac{4 sqrt{x-y} }{x-y}$
$frac{16}{ sqrt{a} + sqrt{6} } = frac{16( sqrt{a}- sqrt{6} ) }{( sqrt{a}+ sqrt{6})( sqrt{a} - sqrt{6}) } = frac{16 sqrt{a}- 16sqrt{6} }{( sqrt{a} )^2- ( sqrt{6})^2 } = frac{16 sqrt{a} -16 sqrt{6} }{a-6} \ \ frac{a}{ sqrt{c}-4} = frac{a (sqrt{c}+4) }{( sqrt{c}-4)( sqrt{c} +4) } = frac{a sqrt{c}+4a }{c-16}$

536.
$frac{18}{2 sqrt{3}+3 } = frac{18(2 sqrt{3}-3) }{(2 sqrt{3} +3)( 2 sqrt{3}-3) } = frac{36 sqrt{3}-54 }{(2 sqrt{3})^2- 9} = frac{3(12 sqrt{3}-18) }{3} = 12 sqrt{3} -18$

$frac{11}{3 sqrt{5} -1} = frac{11(3 sqrt{5}+1)}{(3 sqrt{5}-1)(3 sqrt{5} +1)} = frac{33 sqrt{5} +11}{3^2 *5-1^2} = frac{33 sqrt{5}+11 }{44} = frac{11(3 sqrt{5}+1) }{11*4} = \ \ = frac{3 sqrt{5}+1 }{4}$

$frac{16}{ sqrt{2}+ sqrt{3} +1 } = frac{16( sqrt{2}- sqrt{3} -1) }{( sqrt{2}+ sqrt{3}+1)( sqrt{2} - sqrt{3} -1) } = \ \ = frac{16 sqrt{2} -16 sqrt{3}-16 }{2- sqrt{6}- sqrt{2}+ sqrt{6} -3- sqrt{3} + sqrt{2}- sqrt{3}-1 } = frac{-2(8 sqrt{2}+8 sqrt{3}+8) }{-2} = \ \ =8( sqrt{2} + sqrt{3} +1)$