Solve sqrt{4*5^2+6^2*55^2}

$$\sqrt{ 4 \times { 5 }^{ 2 } + { 6 }^{ 2 } \times { 55 }^{ 2 } }$$

Evaluate

$$10\sqrt{1090}\approx 330.151480384$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt{4\times 25+6^{2}\times 55^{2}}$$

Multiply 4 and 25 to get 100.

$$\sqrt{100+6^{2}\times 55^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\sqrt{100+36\times 55^{2}}$$

Calculate 55 to the power of 2 and get 3025.

$$\sqrt{100+36\times 3025}$$

Multiply 36 and 3025 to get 108900.

$$\sqrt{100+108900}$$

Add 100 and 108900 to get 109000.

$$\sqrt{109000}$$

Factor 109000=10^{2}\times 1090. Rewrite the square root of the product \sqrt{10^{2}\times 1090} as the product of square roots \sqrt{10^{2}}\sqrt{1090}. Take the square root of 10^{2}.

$$10\sqrt{1090}$$