Solve 1.6sqrt{12}+5sqrt{8}2sqrt{3}

$$1.6 \sqrt { 12 } + 5 \sqrt { 8 } 2 \sqrt { 3 }$$

Evaluate

$$\frac{16\sqrt{3}}{5}+20\sqrt{6}\approx 54.53235744$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$1.6\times 2\sqrt{3}+2\times 5\sqrt{8}\sqrt{3}$$

Multiply 1.6 and 2 to get 3.2.

$$3.2\sqrt{3}+2\times 5\sqrt{8}\sqrt{3}$$

Multiply 2 and 5 to get 10.

$$3.2\sqrt{3}+10\sqrt{8}\sqrt{3}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$3.2\sqrt{3}+10\times 2\sqrt{2}\sqrt{3}$$

Multiply 10 and 2 to get 20.

$$3.2\sqrt{3}+20\sqrt{2}\sqrt{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$3.2\sqrt{3}+20\sqrt{6}$$