Question

the question is in the attached file

Answer 1

Answer:

D. 3.2553

Step-by-step explanation:

3/3.65 + 2/0.822

0.8219 + 2.4330

3.2553

Answer 2

Answer:

$\sf D) \quad 3.2553$

Step-by-step explanation:

Simplify the given expression:

   $\sf \dfrac{3}{\sqrt{5}+\sqrt{2}}+\dfrac{2}{\sqrt{5}-\sqrt{2}}$

$\sf = \dfrac{3(\sqrt{5}-\sqrt{2})}{(\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2})}+\dfrac{2(\sqrt{5}+\sqrt{2})}{(\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2})}$

$\sf = \dfrac{3(\sqrt{5}-\sqrt{2})}{3}+\dfrac{2(\sqrt{5}+\sqrt{2})}{3}$

$\sf = \dfrac{3\sqrt{5}-3\sqrt{2}+2\sqrt{5}+2\sqrt{2}}{3}$

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

Given:

• $\sf \sqrt{5} = 2.236$

• $\sf \sqrt{2} = 1.414$

Substitute the given values into the simplified expression:

$\sf =\dfrac{5(2.236)-1.414}{3}$

$\sf =\dfrac{11.18-1.414}{3}$

$\sf =\dfrac{9.766}{3}$

$\sf =3.2553\:\:(4\:d.p.)$