Solve sqrt{(-5)^2*2^2*2}

$$\sqrt { ( - 5 ) ^ { 2 } \times 2 ^ { 2 } \times 2 }$$

Evaluate

$$10\sqrt{2}\approx 14.142135624$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\sqrt{\left(-5\right)^{2}\times 2^{3}}$$

Calculate -5 to the power of 2 and get 25.

$$\sqrt{25\times 2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\sqrt{25\times 8}$$

Multiply 25 and 8 to get 200.

$$\sqrt{200}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$10\sqrt{2}$$