Solve sqrt{53,5^2+36,5^2}

$$\sqrt { 53,5 ^ { 2 } + 36,5 ^ { 2 } }$$

Evaluate

$$5\sqrt{89}\approx 47.16990566$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt{53\times 25+36\times 5^{2}}$$

Multiply 53 and 25 to get 1325.

$$\sqrt{1325+36\times 5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{1325+36\times 25}$$

Multiply 36 and 25 to get 900.

$$\sqrt{1325+900}$$

Add 1325 and 900 to get 2225.

$$\sqrt{2225}$$

Factor 2225=5^{2}\times 89. Rewrite the square root of the product \sqrt{5^{2}\times 89} as the product of square roots \sqrt{5^{2}}\sqrt{89}. Take the square root of 5^{2}.

$$5\sqrt{89}$$