Solve sqrt{2*8}-sqrt{(-3)^2+3sqrt{(3)^2}}

$$\sqrt { 2 \times 8 } - \sqrt { ( - 3 ) ^ { 2 } + 3 \sqrt { ( 3 ) ^ { 2 } } }$$

Evaluate

$$4-3\sqrt{2}\approx -0.242640687$$

Solution Steps

Multiply 2 and 8 to get 16.

$$\sqrt{16}-\sqrt{\left(-3\right)^{2}+3\sqrt{3^{2}}}$$

Calculate the square root of 16 and get 4.

$$4-\sqrt{\left(-3\right)^{2}+3\sqrt{3^{2}}}$$

Calculate -3 to the power of 2 and get 9.

$$4-\sqrt{9+3\sqrt{3^{2}}}$$

Calculate 3 to the power of 2 and get 9.

$$4-\sqrt{9+3\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$4-\sqrt{9+3\times 3}$$

Multiply 3 and 3 to get 9.

$$4-\sqrt{9+9}$$

Add 9 and 9 to get 18.

$$4-\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$4-3\sqrt{2}$$