Question

Find the value of√((2+√3 )/(2-√3)), if √3=1.73

Answer 1

√(2+√3)/(2-√3) => √(2+√3)/√(2-√3)
rationalizing the denominator
√(2+√3)(2+√3)/√(2-√3)(2+√3)
√(2+√3)²/√(2)²-(√3)²
2+√3/√(4-3) => 2+√3/√1. (√1 = 1)
=> 2+√3
since √3 =1.73.
2+√3 = 2+1.73 = 3.73 is the answer
hope this helps

Answer 2

The value of $\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}} }$ is 3.73.

Step-by-step explanation:

We have,

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

To find, the value of $\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}$ = ?

Rationalising numerator and denominator, we get

$\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}\times\dfrac{2+\sqrt{3}}{2+\sqrt{3} }$

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

[ ∵ $a^{2} -b^{2} =(a+b)(a-b)$]

$=\sqrt{\dfrac{(2+\sqrt{3})^{2} }{4 -3}$

$=\sqrt{\dfrac{(2+\sqrt{3})^{2} }{1}$

$=2+\sqrt{3}$

= 2 + 1.73 [∵ $\sqrt{3}$ = 1.73]

= 3.73

Hence, the value of $\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}} }$ is 3.73.