Answer: [tex]4\sqrt{2}+10[/tex]
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Let [tex]x = \sqrt{8}[/tex]
We can replace every square root of 8 with x, since we have that equation above. We end up with 3-x+7+3x. This simplifies to 2x+10 after combining like terms.
Now we can reintoduce the square root back in
[tex]2x+10 = 2\sqrt{8}+10[/tex]
The use of x is optional as you can combine like terms directly. However, it might help to make the temporary replacement.
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Now simplify the square root
[tex]\sqrt{8} = \sqrt{4*2}[/tex]
[tex]\sqrt{8} = \sqrt{4}*\sqrt{2}[/tex]
[tex]\sqrt{8} = 2\sqrt{2}[/tex]
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Therefore,
[tex]2\sqrt{8}+10[/tex]
turns into
[tex]2*2\sqrt{2}+10[/tex]
[tex]4\sqrt{2}+10[/tex]
