Question

(√98 - √50)³

"conta por favor"

Answer 1

$( \sqrt{98} - \sqrt{50} )^3= \\ \\ = (\sqrt{7^2.2} - \sqrt{5^2.2} )^3= \\ \\ =( \sqrt{7^2} . \sqrt{2} - \sqrt{5^2} . \sqrt{2} )^3= \\ \\ =(7 \sqrt{2} - 5 \sqrt{2} )^3= \\ \\=(2 \sqrt{2} )^3=2^3.( \sqrt{2} )^3=2^3.( 2^{ \frac{1}{2} } )^3=2^3. 2^{ \frac{3}{2} } = 2^{(3+ \frac{3}{2} )} = 2^{( \frac{6+3}{2}) } = 2^{ \frac{9}{2} } = \\ \\ = \sqrt{2^9} = \sqrt{2^8.2} =2^4 \sqrt{2} =16 \sqrt{2}$