Solve 6sqrt{2}*2sqrt{17}*(3sqrt{2}+17)

$$6 \sqrt{ 2 } \times 2 \sqrt{ 17 } \times (3 \sqrt{ 2 } +17)$$

Evaluate

$$12\sqrt{17}\left(17\sqrt{2}+6\right)\approx 1486.377791593$$

Solution Steps

Multiply 2 and 6 to get 12.

$$12\sqrt{2}\sqrt{17}\left(3\sqrt{2}+17\right)$$

To multiply \sqrt{2} and \sqrt{17}, multiply the numbers under the square root.

$$12\sqrt{34}\left(3\sqrt{2}+17\right)$$

Use the distributive property to multiply 12\sqrt{34} by 3\sqrt{2}+17.

$$36\sqrt{2}\sqrt{34}+204\sqrt{34}$$

Factor 34=2\times 17. Rewrite the square root of the product \sqrt{2\times 17} as the product of square roots \sqrt{2}\sqrt{17}.

$$36\sqrt{2}\sqrt{2}\sqrt{17}+204\sqrt{34}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$36\times 2\sqrt{17}+204\sqrt{34}$$

Multiply 36 and 2 to get 72.

$$72\sqrt{17}+204\sqrt{34}$$