Solve sqrt{7*3*2*2*2*2*2*2}

$$\sqrt{ 7 \times 3 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 }$$

Evaluate

$$8\sqrt{21}\approx 36.66060556$$

Solution Steps

Multiply 7 and 3 to get 21.

$$\sqrt{21\times 2\times 2\times 2\times 2\times 2\times 2}$$

Multiply 21 and 2 to get 42.

$$\sqrt{42\times 2\times 2\times 2\times 2\times 2}$$

Multiply 42 and 2 to get 84.

$$\sqrt{84\times 2\times 2\times 2\times 2}$$

Multiply 84 and 2 to get 168.

$$\sqrt{168\times 2\times 2\times 2}$$

Multiply 168 and 2 to get 336.

$$\sqrt{336\times 2\times 2}$$

Multiply 336 and 2 to get 672.

$$\sqrt{672\times 2}$$

Multiply 672 and 2 to get 1344.

$$\sqrt{1344}$$

Factor 1344=8^{2}\times 21. Rewrite the square root of the product \sqrt{8^{2}\times 21} as the product of square roots \sqrt{8^{2}}\sqrt{21}. Take the square root of 8^{2}.

$$8\sqrt{21}$$