Solve (2sqrt{3})*(3sqrt{3}+4sqrt{20})

$$( 2 \sqrt { 3 } ) \cdot ( 3 \sqrt { 3 } + 4 \sqrt { 20 } )$$

Evaluate

$$16\sqrt{15}+18\approx 79.967733539$$

Solution Steps

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}.

$$2\sqrt{3}\left(3\sqrt{3}+4\times 2\sqrt{5}\right)$$

Multiply 4 and 2 to get 8.

$$2\sqrt{3}\left(3\sqrt{3}+8\sqrt{5}\right)$$

Use the distributive property to multiply 2\sqrt{3} by 3\sqrt{3}+8\sqrt{5}.

$$6\left(\sqrt{3}\right)^{2}+16\sqrt{3}\sqrt{5}$$

The square of \sqrt{3} is 3.

$$6\times 3+16\sqrt{3}\sqrt{5}$$

Multiply 6 and 3 to get 18.

$$18+16\sqrt{3}\sqrt{5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$18+16\sqrt{15}$$