Answer:
[tex]5\sqrt{10}+\sqrt{40} +\sqrt{90}=10\sqrt{10}[/tex]
Step-by-step explanation:
We have the following expression:
[tex]5\sqrt{10}+\sqrt{40} +\sqrt{90}[/tex]
Remember the property of root multiplication:
[tex]\sqrt[n]{x*y}=\sqrt[n]{x}\sqrt[n]{y}[/tex]
Therefore:
[tex]\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}[/tex]
Also:
[tex]\sqrt{90}=\sqrt{9*10}=\sqrt{9}*\sqrt{10}=3\sqrt{10}[/tex]
Then we have that:
[tex]5\sqrt{10}+\sqrt{40} +\sqrt{90}=5\sqrt{10}+2\sqrt{10}+3\sqrt{10}[/tex]
Remember the property of sum of roots:
[tex]a\sqrt{b}+2a\sqrt{b}=3a\sqrt{b}[/tex]
Finally:
[tex]5\sqrt{10}+\sqrt{40} +\sqrt{90}=(5+2+3)\sqrt{10}[/tex]
[tex]5\sqrt{10}+\sqrt{40} +\sqrt{90}=10\sqrt{10}[/tex]
