Question

√[-√3+√{84+18√3}] what is right value this questions

Answer 1

Answer for this question is 3.

(84+18√3) = (9+√3)^2 ,,,so by solving we √3 cancels out and we get √9 = 3 as answer

Answer 2

The value of $\sqrt{[-\sqrt{3}+\sqrt{84+18\sqrt{3}}}]=3.$

Step-by-step explanation:

We have,

$\sqrt{[-\sqrt{3}+\sqrt{84+18\sqrt{3}}}]$

To find, the value of $\sqrt{[-\sqrt{3}+\sqrt{84+18\sqrt{3}}}]=?$

∴ $\sqrt{[-\sqrt{3}+\sqrt{84+18\sqrt{3}}}}$

$=\sqrt{[-\sqrt{3}+\sqrt{81+3+18\sqrt{3}}}]$

$=\sqrt{[-\sqrt{3}+\sqrt{9^2+\sqrt{3}^3+2(9)(\sqrt{3}}})]$

$=\sqrt{[-\sqrt{3}+\sqrt{(9+\sqrt{3})^2)]$

Using algebraic identity,

$(a+b)^{2}=a^{2}+b^{2}+2ab$

$=\sqrt{[-\sqrt{3}+9+\sqrt{3}]$

$=\sqrt{9}$

= 3

Hence, the value of $\sqrt{[-\sqrt{3}+\sqrt{84+18\sqrt{3}}}]=3.$