Solve 4sqrt{99}(2sqrt{66}-3sqrt{6})

$$4 \sqrt{ 99 } (2 \sqrt{ 66 } -3 \sqrt{ 6 } )$$

Evaluate

$$264\sqrt{6}-36\sqrt{66}\approx 354.199909528$$

Solution Steps

Factor 99=3^{2}\times 11. Rewrite the square root of the product \sqrt{3^{2}\times 11} as the product of square roots \sqrt{3^{2}}\sqrt{11}. Take the square root of 3^{2}.

$$4\times 3\sqrt{11}\left(2\sqrt{66}-3\sqrt{6}\right)$$

Multiply 4 and 3 to get 12.

$$12\sqrt{11}\left(2\sqrt{66}-3\sqrt{6}\right)$$

Use the distributive property to multiply 12\sqrt{11} by 2\sqrt{66}-3\sqrt{6}.

$$24\sqrt{11}\sqrt{66}-36\sqrt{11}\sqrt{6}$$

Factor 66=11\times 6. Rewrite the square root of the product \sqrt{11\times 6} as the product of square roots \sqrt{11}\sqrt{6}.

$$24\sqrt{11}\sqrt{11}\sqrt{6}-36\sqrt{11}\sqrt{6}$$

Multiply \sqrt{11} and \sqrt{11} to get 11.

$$24\times 11\sqrt{6}-36\sqrt{11}\sqrt{6}$$

Multiply 24 and 11 to get 264.

$$264\sqrt{6}-36\sqrt{11}\sqrt{6}$$

To multiply \sqrt{11} and \sqrt{6}, multiply the numbers under the square root.

$$264\sqrt{6}-36\sqrt{66}$$