Question

find the value of square root 2+root 3 ÷ 2-root 3 if root 3 =1.73

Answer 1

the answer is in the pic

Answer 2

Answer:

Value of  $\frac{\sqrt{2}+\sqrt{3}}{2-\sqrt{3}}=6.46+3.73\sqrt{2}$

Step-by-step explanation:

Given: √3 = 1.73

           $\frac{\sqrt{2}+\sqrt{3}}{2-\sqrt{3}}$

To find: Value of given Expression

we rationalize the denominator given expression,

$\frac{\sqrt{2}+\sqrt{3}}{2-\sqrt{3}}$

$\implies\frac{\sqrt{2}+\sqrt{3}}{2-\sqrt{3}}\times\frac{2+\sqrt{3}}{2+\sqrt{3}}$

$\implies\frac{(\sqrt{2}+\sqrt{3})(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3})}$

$\implies\frac{\sqrt{2}(2+\sqrt{3})+\sqrt{3}(2+\sqrt{3})}{(2)^2-(\sqrt{3})^2}$

$\implies\frac{2\sqrt{2}+\sqrt{6}+2\sqrt{3}+3}{4-3}$

$\implies2\sqrt{2}+\sqrt{6}+2\sqrt{3}+3$

$\implies2\sqrt{2}+1.73\sqrt{2}+2\times1.73+3$

$\implies6.46+3.73\sqrt{2}$

Therfore, Value of  $\frac{\sqrt{2}+\sqrt{3}}{2-\sqrt{3}}=6.46+3.73\sqrt{2}$