Question

$$\sqrt{10+\sqrt{25+\sqrt{108+154+\sqrt{225}}}=?$$

Answer

sqrt(10)+174+6*sqrt(3)

Solution


Since \(5\times 5=25\), the square root of \(25\) is \(5\).
\[\sqrt{10}+5+\sqrt{108}+154+\sqrt{225}\]
Simplify  \(\sqrt{108}\)  to  \(6\sqrt{3}\).
\[\sqrt{10}+5+6\sqrt{3}+154+\sqrt{225}\]
Since \(15\times 15=225\), the square root of \(225\) is \(15\).
\[\sqrt{10}+5+6\sqrt{3}+154+15\]
Collect like terms.
\[\sqrt{10}+(5+154+15)+6\sqrt{3}\]
Simplify.
\[\sqrt{10}+174+6\sqrt{3}\]

Decimal Form: 187.554583