Solve 4:(1)sqrt{24}*sqrt{3}-4*sqrt{8}

$$4 : ( 1 ) \sqrt { 24 } \times \sqrt { 3 } - 4 \times \sqrt { 8 }$$

Evaluate

$$16\sqrt{2}\approx 22.627416998$$

Solution Steps

Factor 24=3\times 8. Rewrite the square root of the product \sqrt{3\times 8} as the product of square roots \sqrt{3}\sqrt{8}.

$$\frac{4}{1}\sqrt{3}\sqrt{8}\sqrt{3}-4\sqrt{8}$$

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

$$\frac{4}{1}\times 3\sqrt{8}-4\sqrt{8}$$

Anything divided by one gives itself.

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

Multiply 4 and 3 to get 12.

$$12\sqrt{8}-4\sqrt{8}$$

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}.

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

Multiply 12 and 2 to get 24.

$$24\sqrt{2}-4\sqrt{8}$$

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}.

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

Multiply -4 and 2 to get -8.

$$24\sqrt{2}-8\sqrt{2}$$

Combine 24\sqrt{2} and -8\sqrt{2} to get 16\sqrt{2}.

$$16\sqrt{2}$$