Solve sqrt{(2*3^2/3*3)^2}+sqrt{(6*2^2/8-4)^2}

$$\sqrt { ( \frac { 2 \times 3 ^ { 2 } } { 3 \times 3 } ) ^ { 2 } } + \sqrt { ( \frac { 6 \times 2 ^ { 2 } } { 8 - 4 } ) ^ { 2 } }$$

Evaluate

$$8$$

Solution Steps

Cancel out 3\times 3 in both numerator and denominator.

$$\sqrt{2^{2}}+\sqrt{\left(\frac{6\times 2^{2}}{8-4}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4}+\sqrt{\left(\frac{6\times 2^{2}}{8-4}\right)^{2}}$$

Calculate the square root of 4 and get 2.

$$2+\sqrt{\left(\frac{6\times 2^{2}}{8-4}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$2+\sqrt{\left(\frac{6\times 4}{8-4}\right)^{2}}$$

Multiply 6 and 4 to get 24.

$$2+\sqrt{\left(\frac{24}{8-4}\right)^{2}}$$

Subtract 4 from 8 to get 4.

$$2+\sqrt{\left(\frac{24}{4}\right)^{2}}$$

Divide 24 by 4 to get 6.

$$2+\sqrt{6^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$2+\sqrt{36}$$

Calculate the square root of 36 and get 6.

$$2+6$$

Add 2 and 6 to get 8.

$$8$$

Factor

$$2^{3}$$