Answer :
[tex]12\sqrt{18}-6\sqrt{20}-3\sqrt{45}=12\sqrt{9\cdot2}-6\sqrt{4\cdot5}-3\sqrt{9\cdot5}\\\\=12\cdot3\sqrt2-6\cdot2\sqrt5-3\cdot3\sqrt5=36\sqrt2-12\sqrt5-9\sqrt5\\\\=36\sqrt2-21\sqrt5[/tex]
Answer:
[tex]12 \sqrt{18} - 6\sqrt{20}-3\sqrt{50}+8\sqrt{45}=21\sqrt{2} + 12\sqrt{5}[/tex]
Step-by-step explanation:
Given :[tex]12 \sqrt{18} - 6\sqrt{20}-3\sqrt{50}+8\sqrt{45}[/tex]
To Find : Simplify
Solution:
[tex]12 \sqrt{18} - 6\sqrt{20}-3\sqrt{50}+8\sqrt{45}[/tex]
[tex]12 \sqrt{2 \times 3 \times 3} - 6\sqrt{2 \times 2 \times 5}-3\sqrt{5 \times 5 \times 2}+8\sqrt{3 \times 3 \times 5}[/tex]
[tex](12 \times 3) \sqrt{2} - (6 \times 2) \sqrt{5}-(3 \times 5)\sqrt{2}+(8 \times 3)\sqrt{5}[/tex]
[tex]36\sqrt{2} - 12\sqrt{5}-15\sqrt{2}+24\sqrt{5}[/tex]
[tex]21\sqrt{2} + 12\sqrt{5}[/tex]
So, [tex]12 \sqrt{18} - 6\sqrt{20}-3\sqrt{50}+8\sqrt{45}=21\sqrt{2} + 12\sqrt{5}[/tex]