Solve 4sqrt{27}*5sqrt{6}

$$4 \sqrt { 27 } \cdot 5 \sqrt { 6 }$$

Evaluate

$$180\sqrt{2}\approx 254.558441227$$

Solution Steps

Multiply 4 and 5 to get 20.

$$20\sqrt{27}\sqrt{6}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$20\times 3\sqrt{3}\sqrt{6}$$

Multiply 20 and 3 to get 60.

$$60\sqrt{3}\sqrt{6}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$60\sqrt{3}\sqrt{3}\sqrt{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$60\times 3\sqrt{2}$$

Multiply 60 and 3 to get 180.

$$180\sqrt{2}$$