Solve 9sqrt{32^2}-2sqrt{27}-2sqrt{7}

$$9 \sqrt{ { 32 }^{ 2 } } -2 \sqrt{ 27 } -2 \sqrt{ 7 }$$

Evaluate

$$288-2\sqrt{7}-6\sqrt{3}\approx 272.316192532$$

Solution Steps

Calculate 32 to the power of 2 and get 1024.

$$9\sqrt{1024}-2\sqrt{27}-2\sqrt{7}$$

Calculate the square root of 1024 and get 32.

$$9\times 32-2\sqrt{27}-2\sqrt{7}$$

Multiply 9 and 32 to get 288.

$$288-2\sqrt{27}-2\sqrt{7}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$288-2\times 3\sqrt{3}-2\sqrt{7}$$

Multiply -2 and 3 to get -6.

$$288-6\sqrt{3}-2\sqrt{7}$$