Question

$$3 \sqrt{ 20 } + \sqrt{ 28 } + \sqrt{ 45 } - \sqrt{ 63 }$$

Answer

9*sqrt(5)-sqrt(7)

Solution


Simplify  \(\sqrt{20}\)  to  \(2\sqrt{5}\).
\[3\times 2\sqrt{5}+\sqrt{28}+\sqrt{45}-\sqrt{63}\]
Simplify  \(\sqrt{28}\)  to  \(2\sqrt{7}\).
\[3\times 2\sqrt{5}+2\sqrt{7}+\sqrt{45}-\sqrt{63}\]
Simplify  \(\sqrt{45}\)  to  \(3\sqrt{5}\).
\[3\times 2\sqrt{5}+2\sqrt{7}+3\sqrt{5}-\sqrt{63}\]
Simplify  \(\sqrt{63}\)  to  \(3\sqrt{7}\).
\[3\times 2\sqrt{5}+2\sqrt{7}+3\sqrt{5}-3\sqrt{7}\]
Simplify  \(3\times 2\sqrt{5}\)  to  \(6\sqrt{5}\).
\[6\sqrt{5}+2\sqrt{7}+3\sqrt{5}-3\sqrt{7}\]
Collect like terms.
\[(6\sqrt{5}+3\sqrt{5})+(2\sqrt{7}-3\sqrt{7})\]
Simplify.
\[9\sqrt{5}-\sqrt{7}\]

Decimal Form: 17.478860