Question

please solve the question no.2
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Answer 1

Answer:

6

Step-by-step explanation:

Given :

To find the value of :

$\sqrt{12 + 6\sqrt{3}} +\sqrt{12 - 6\sqrt{3}}$

Solution :

We know that,

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

Hence,

By using them,

$\sqrt{12 + 6\sqrt{3}} +\sqrt{12 - 6\sqrt{3}}$

⇒ $\sqrt{9 + 3 + 6\sqrt{3}} +\sqrt{9 + 3 - 6\sqrt{3}}$

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

⇒ $\sqrt{( 3 + \sqrt{3})^2} + \sqrt{( 3 - \sqrt{3})^2}= (3 + \sqrt{3}) + ( 3 - \sqrt{3}) = 6$