Solve 3sqrt{4}(2sqrt{32})-2sqrt{6}(4sqrt{3})

$$3 \sqrt { 4 } ( 2 \sqrt { 32 } ) - 2 \sqrt { 6 } ( 4 \sqrt { 3 } )$$

Evaluate

$$24\sqrt{2}\approx 33.941125497$$

Solution Steps

Factor 32=4\times 8. Rewrite the square root of the product \sqrt{4\times 8} as the product of square roots \sqrt{4}\sqrt{8}.

$$3\sqrt{4}\times 2\sqrt{4}\sqrt{8}-2\sqrt{6}\times 4\sqrt{3}$$

Multiply \sqrt{4} and \sqrt{4} to get 4.

$$3\times 4\times 2\sqrt{8}-2\sqrt{6}\times 4\sqrt{3}$$

Multiply 3 and 4 to get 12.

$$12\times 2\sqrt{8}-2\sqrt{6}\times 4\sqrt{3}$$

Multiply 12 and 2 to get 24.

$$24\sqrt{8}-2\sqrt{6}\times 4\sqrt{3}$$

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}.

$$24\times 2\sqrt{2}-2\sqrt{6}\times 4\sqrt{3}$$

Multiply 24 and 2 to get 48.

$$48\sqrt{2}-2\sqrt{6}\times 4\sqrt{3}$$

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}.

$$48\sqrt{2}-2\sqrt{3}\sqrt{2}\times 4\sqrt{3}$$

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

$$48\sqrt{2}-2\times 3\times 4\sqrt{2}$$

Multiply 2 and 3 to get 6.

$$48\sqrt{2}-6\times 4\sqrt{2}$$

Multiply 6 and 4 to get 24.

$$48\sqrt{2}-24\sqrt{2}$$

Combine 48\sqrt{2} and -24\sqrt{2} to get 24\sqrt{2}.

$$24\sqrt{2}$$