Solve sqrt{36*(6-2)^2/5^2*2^4}

$$\sqrt { \frac { 36 \times ( 6 - 2 ) ^ { 2 } } { 5 ^ { 2 } \times 2 ^ { 4 } } }$$

Evaluate

$$\frac{6}{5}=1.2$$

Solution Steps

Subtract 2 from 6 to get 4.

$$\sqrt{\frac{36\times 4^{2}}{5^{2}\times 2^{4}}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{\frac{36\times 16}{5^{2}\times 2^{4}}}$$

Multiply 36 and 16 to get 576.

$$\sqrt{\frac{576}{5^{2}\times 2^{4}}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{\frac{576}{25\times 2^{4}}}$$

Calculate 2 to the power of 4 and get 16.

$$\sqrt{\frac{576}{25\times 16}}$$

Multiply 25 and 16 to get 400.

$$\sqrt{\frac{576}{400}}$$

Reduce the fraction \frac{576}{400} to lowest terms by extracting and canceling out 16.

$$\sqrt{\frac{36}{25}}$$

Rewrite the square root of the division \frac{36}{25} as the division of square roots \frac{\sqrt{36}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{6}{5}$$

Factor

$$\frac{2 \cdot 3}{5} = 1\frac{1}{5} = 1.2$$