Question

Raționați numitorul: 40 pe 18 totul în radical.

Minus 54 pe 75 totul în radical. Repede plssss

Answer 1

Răspuns: Ai mai jos rezolvarea

Explicație pas cu pas:

Salutare!

• Varianta I de scriere

$\bf \sqrt{\dfrac{40}{18} } - \sqrt{\dfrac{54}{75}} =$

$\bf \sqrt{\dfrac{40}{18}^{(2} } - \sqrt{\dfrac{54}{75}^{(3}} =$

Simplificam cu 2 primul radical si cu 3 al doilea radical

$\bf \sqrt{\dfrac{20}{9}} - \sqrt{\dfrac{18}{25}} =$

$\bf \sqrt{\dfrac{5\cdot2^{2}}{3^{2}}} - \sqrt{\dfrac{2\cdot3^{2}}{5^{2}}} =$

$\bf \dfrac{2\sqrt{5}}{3} -\dfrac{3\sqrt{2}}{5}=$

$\bf \dfrac{5\cdot2\sqrt{5}}{5\cdot3} -\dfrac{3\cdot3\sqrt{2}}{3\cdot5}=$

Aducem la același numitor

$\boxed{\bf \dfrac{10\sqrt{5}-9\sqrt{2}}{15}}$

• Varianta II de scriere

$\bf \sqrt{\dfrac{40}{18} } = \sqrt{\dfrac{5\cdot 2^{3} }{2\cdot3^{2}}} =\dfrac{2\sqrt{10}}{3\sqrt{2}} =\dfrac{2\sqrt{10}}{3\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{2\sqrt{20}}{3\cdot 2} =\dfrac{\not2\sqrt{20}}{3\cdot \not2} =\dfrac{\sqrt{20}}{3}=\boxed{\bf \dfrac{2\sqrt{5}}{3}}$

$\bf \sqrt{\dfrac{54}{75} } = \sqrt{\dfrac{2\cdot 3^{3} }{3\cdot5^{2}}} =\dfrac{3\sqrt{6}}{5\sqrt{3}} =\dfrac{3\sqrt{6}}{5\sqrt{3}}\cdot \dfrac{\sqrt{3}}{\sqrt{3}}=\dfrac{3\sqrt{18}}{5\cdot 3} =\dfrac{\not3\sqrt{18}}{5\cdot \not3} =\dfrac{\sqrt{18}}{5}=\boxed{\bf \dfrac{3\sqrt{2}}{5}}$

#copaceibrainly

Answer 2

Răspuns:

√(40/18) = √40 / √18 =  √(4×10) / √(9×2) = 2√10 / 3√2 = 2√10×√2 / 3√2 × √2 = 2√20 / 3×2 =

2√20 / 6 = √20 / 3

(am rationalizat  fractia cu √2 )

- √(54/75) = - ( √54 / √75) = - (√(9×6) / √(25×3)) = - (3√6 / 5√3) = - (3√6×√3 / 5√3 × √3)  = - (3√18 / 5×3) = - (3×3√2 / 15)  = - ( 3√2 / 5)  

(am rationalizat fractia cu √3 )

#copaceibrainly