Answer:
[tex]36+14\sqrt{6}[/tex]
Step-by-step explanation:
[tex](\sqrt{8}+\sqrt{12})(\sqrt{48}+\sqrt{18})[/tex]
First step: Multiply/Distribute (you can say "F.O.I.L")
[tex]\sqrt{8}(\sqrt{48}+\sqrt{18})+\sqrt{12}(\sqrt{48}+\sqrt{18})[/tex]
[tex]\sqrt{8} \sqrt{48}+\sqrt{8} \sqrt{18}+\sqrt{12}\sqrt{48}+\sqrt{12}\sqrt{18}[/tex]
Second step: As long as [tex]a,b[/tex] are positive or zero then [tex]\sqrt{a}\sqrt{b}=\sqrt{a \cdot b}[/tex]
[tex]\sqrt{ 8 \cdot 48}+\sqrt{8 \cdot 18}+\sqrt{12 \cdot 48}+\sqrt{12 \cdot 18}[/tex]
Third step: Let's look for perfect square factors inside the square root symbols.
[tex]\sqrt{8 \cdot (8 \cdot 6)}+\sqrt{(4 \cdot 2) \cdot (9 \cdot2)}+\sqrt{(4 \cdot 3) \cdot (16 \cdot 3)}+\sqrt{(4 \cdot 3) \cdot (9 \cdot 2)}[/tex]
[tex]\sqrt{8^2 \cdot 6}+\sqrt{4 \cdot 9 \cdot 2^2}+\sqrt{4 \cdot 16 \cdot 3^2}+\sqrt{4 \cdot 9 \cdot 3 \cdot 2}[/tex]
Fourth step: Simplify the square root of perfect squares and also recall the property in step 2.
[tex]8 \sqrt{6}+2 \cdot 3 \cdot 2 +2\cdot 4 \cdot 3+2 \cdot 3 \sqrt{3 \cdot 2}[/tex]
Fifth step: Terms are separated by addition and subtraction symbols. Look at each term and see if there is anything to simplify outside the square root and then look inside the square root.
[tex]8 \sqrt{6}+12 +24+6 \sqrt{6}[/tex]
Sixth step: Add "like terms". Add your terms with out the square roots together. Add your terms with [tex]\sqrt{6}[/tex] together.
[tex]8 \sqrt{6}+6 \sqrt{6}+12+24[/tex]
[tex](8+6)\sqrt{6}+(12+24)[/tex]
[tex]14\sqrt{6}+36[/tex]
[tex]36+14\sqrt{6}[/tex]
