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

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

Evaluate

$$42\sqrt{2}\approx 59.39696962$$

Solution Steps

Multiply 7 and 3 to get 21.

$$\sqrt{21\times 3\times 2\times 2\times 2\times 7}$$

Multiply 21 and 3 to get 63.

$$\sqrt{63\times 2\times 2\times 2\times 7}$$

Multiply 63 and 2 to get 126.

$$\sqrt{126\times 2\times 2\times 7}$$

Multiply 126 and 2 to get 252.

$$\sqrt{252\times 2\times 7}$$

Multiply 252 and 2 to get 504.

$$\sqrt{504\times 7}$$

Multiply 504 and 7 to get 3528.

$$\sqrt{3528}$$

Factor 3528=42^{2}\times 2. Rewrite the square root of the product \sqrt{42^{2}\times 2} as the product of square roots \sqrt{42^{2}}\sqrt{2}. Take the square root of 42^{2}.

$$42\sqrt{2}$$