Solve sqrt{5^3*2^6*5^4}

$$\sqrt { 5 ^ { 3 } \times 2 ^ { 6 } \times 5 ^ { 4 } }$$

Evaluate

$$1000\sqrt{5}\approx 2236.0679775$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\sqrt{5^{7}\times 2^{6}}$$

Calculate 5 to the power of 7 and get 78125.

$$\sqrt{78125\times 2^{6}}$$

Calculate 2 to the power of 6 and get 64.

$$\sqrt{78125\times 64}$$

Multiply 78125 and 64 to get 5000000.

$$\sqrt{5000000}$$

Factor 5000000=1000^{2}\times 5. Rewrite the square root of the product \sqrt{1000^{2}\times 5} as the product of square roots \sqrt{1000^{2}}\sqrt{5}. Take the square root of 1000^{2}.

$$1000\sqrt{5}$$