Question

$$( \sqrt{ 20- \sqrt{ 45) \times \sqrt{ 5 } } }$$

Answer

sqrt(5)

Solution


Simplify  \(\sqrt{45}\)  to  \(3\sqrt{5}\).
\[\sqrt{20-3\sqrt{5}\sqrt{5}}\]
Simplify  \(3\sqrt{5}\sqrt{5}\)  to  \(3\sqrt{5\times 5}\).
\[\sqrt{20-3\sqrt{5\times 5}}\]
Simplify  \(5\times 5\)  to  \(25\).
\[\sqrt{20-3\sqrt{25}}\]
Since \(5\times 5=25\), the square root of \(25\) is \(5\).
\[\sqrt{20-3\times 5}\]
Simplify  \(3\times 5\)  to  \(15\).
\[\sqrt{20-15}\]
Simplify  \(20-15\)  to  \(5\).
\[\sqrt{5}\]

Decimal Form: 2.236068