Solve sqrt{3*5^2*2^2-5^2}=

$$\sqrt { 3 \cdot 5 ^ { 2 } \cdot 2 ^ { 2 } - 5 ^ { 2 } } =$$

Evaluate

$$5\sqrt{11}\approx 16.583123952$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt{3\times 25\times 2^{2}-5^{2}}$$

Multiply 3 and 25 to get 75.

$$\sqrt{75\times 2^{2}-5^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{75\times 4-5^{2}}$$

Multiply 75 and 4 to get 300.

$$\sqrt{300-5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{300-25}$$

Subtract 25 from 300 to get 275.

$$\sqrt{275}$$

Factor 275=5^{2}\times 11. Rewrite the square root of the product \sqrt{5^{2}\times 11} as the product of square roots \sqrt{5^{2}}\sqrt{11}. Take the square root of 5^{2}.

$$5\sqrt{11}$$