This question was uploaded on 24/10/21 on social media accounts.
Simplify the given equation under the square root. A similar type of question I saw on YouTube. In this, we have to make a complete square under the root so that root can be canceled.
Solution:
Key points to notice:
\[\sqrt6=\sqrt2\times\sqrt3\]
\[\sqrt{10}=\sqrt2\times\sqrt5\]
\[\sqrt{15}=\sqrt3\times\sqrt5\]
This equation is in the form of:
\[\sqrt{(a+b+c)^2}\]
\[\Rightarrow a^2+b^2+c^2=79\]
\[\Rightarrow 2ab=24\sqrt6,⠀2ac=16\sqrt{10},⠀2bc=12\sqrt{15}\]
After solving:
\[\Rightarrow a=4\sqrt2,⠀b=3\sqrt3,⠀c=2\sqrt5\]
\[\Rightarrow \sqrt{24\sqrt6+16\sqrt{10}+12\sqrt{15}+79}\]
\[=4\sqrt2+3\sqrt3+2\sqrt5\]
Question related to Algebra, Equation.
