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\left(\sqrt{15}\right)^{2}+4\sqrt{15}\sqrt{3}+4\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{15}+2\sqrt{3}\right)^{2}.
15+4\sqrt{15}\sqrt{3}+4\left(\sqrt{3}\right)^{2}
The square of \sqrt{15} is 15.
15+4\sqrt{3}\sqrt{5}\sqrt{3}+4\left(\sqrt{3}\right)^{2}
Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.
15+4\times 3\sqrt{5}+4\left(\sqrt{3}\right)^{2}
Multiply \sqrt{3} and \sqrt{3} to get 3.
15+12\sqrt{5}+4\left(\sqrt{3}\right)^{2}
Multiply 4 and 3 to get 12.
15+12\sqrt{5}+4\times 3
The square of \sqrt{3} is 3.
15+12\sqrt{5}+12
Multiply 4 and 3 to get 12.
27+12\sqrt{5}
Add 15 and 12 to get 27.
\left(\sqrt{15}\right)^{2}+4\sqrt{15}\sqrt{3}+4\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{15}+2\sqrt{3}\right)^{2}.
15+4\sqrt{15}\sqrt{3}+4\left(\sqrt{3}\right)^{2}
The square of \sqrt{15} is 15.
15+4\sqrt{3}\sqrt{5}\sqrt{3}+4\left(\sqrt{3}\right)^{2}
Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.
15+4\times 3\sqrt{5}+4\left(\sqrt{3}\right)^{2}
Multiply \sqrt{3} and \sqrt{3} to get 3.
15+12\sqrt{5}+4\left(\sqrt{3}\right)^{2}
Multiply 4 and 3 to get 12.
15+12\sqrt{5}+4\times 3
The square of \sqrt{3} is 3.
15+12\sqrt{5}+12
Multiply 4 and 3 to get 12.
27+12\sqrt{5}
Add 15 and 12 to get 27.