Question

Calcula y simplifica:
$5 \sqrt{125}+6 \sqrt{45}-7 \sqrt{20} + \frac{3}{2} \sqrt{80}$

Answer 1

Simplifica

5√125 + 6 √45 - 7√20 + 3/2 √80 =  (125 = 5 * 5 * 5 = 5² * 5)
5√(5² *5) + 6 √(9 * 5) - 7√(4 * 5) + 3/2 √(16*5) =    Aplicas √a*b = √a * √b
5√5²*√5 + 6√9 * √5 - 7√4 * √5 + 3/2 √16 * √5 =
5 * 5√5 + 6 * 3√5 - 7 * 2√5 + 3/2 * 4√5 =
25√25 + 18√5 - 14√5 + 12/2√5 =
25√5 + 18√5 - 14√5 + 6√5 =
43√5 - 14√5 + 6√5 =
29√5 + 6√5 =
35√5

Respuesta.
35√5

Answer 2

$5 \sqrt{125} = 5 \sqrt{5. 5^{2} } =5.5 \sqrt{5} =25 \sqrt{5}$

$6\sqrt{45} = 6 \sqrt{5.3^{2} } = 6.3\sqrt{5} =18 \sqrt{5}$

$7\sqrt{20} =7 \sqrt{5.2^{2} } = 7.2\sqrt{5} =14 \sqrt{5}$

$\frac{3}{2} \sqrt{80} = \sqrt{ 2^{2}. 2^{2}.5 } = \frac{3.2.2}{2} \sqrt{5} =6 \sqrt{5}$

$25 \sqrt{5} +18 \sqrt{5} - 14\sqrt{5} +6 \sqrt{5}$

$35\sqrt{5}$