Solve sqrt{3*7}sqrt{3*2^4}=

$$\sqrt{ 3 \times 7 } \sqrt{ 3 \times { 2 }^{ 4 } } =$$

Evaluate

$$12\sqrt{7}\approx 31.749015733$$

Solution Steps

Multiply 3 and 7 to get 21.

$$\sqrt{21}\sqrt{3\times 2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\sqrt{21}\sqrt{3\times 16}$$

Multiply 3 and 16 to get 48.

$$\sqrt{21}\sqrt{48}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\sqrt{21}\times 4\sqrt{3}$$

Factor 21=3\times 7. Rewrite the square root of the product \sqrt{3\times 7} as the product of square roots \sqrt{3}\sqrt{7}.

$$\sqrt{3}\sqrt{7}\times 4\sqrt{3}$$

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

$$3\times 4\sqrt{7}$$

Multiply 3 and 4 to get 12.

$$12\sqrt{7}$$