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\frac{3}{2}\times 2\sqrt{5}\sqrt{15}\left(-\frac{1}{3}\right)\sqrt{48}
Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.
3\sqrt{5}\sqrt{15}\left(-\frac{1}{3}\right)\sqrt{48}
Cancel out 2 and 2.
-\sqrt{5}\sqrt{15}\sqrt{48}
Cancel out 3 and 3.
-\sqrt{5}\sqrt{15}\times 4\sqrt{3}
Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.
-4\sqrt{5}\sqrt{15}\sqrt{3}
Multiply -1 and 4 to get -4.
-4\sqrt{5}\sqrt{5}\sqrt{3}\sqrt{3}
Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.
-4\times 5\sqrt{3}\sqrt{3}
Multiply \sqrt{5} and \sqrt{5} to get 5.
-4\times 5\times 3
Multiply \sqrt{3} and \sqrt{3} to get 3.
-20\times 3
Multiply -4 and 5 to get -20.
-60
Multiply -20 and 3 to get -60.