Solve sqrt{75}+2sqrt{80}+3sqrt{451}

$$\sqrt { 75 } + 2 \sqrt { 80 } + 3 \sqrt { 451 }$$

Evaluate

$$3\sqrt{451}+5\sqrt{3}+8\sqrt{5}\approx 90.259079603$$

Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$5\sqrt{3}+2\sqrt{80}+3\sqrt{451}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$5\sqrt{3}+2\times 4\sqrt{5}+3\sqrt{451}$$

Multiply 2 and 4 to get 8.

$$5\sqrt{3}+8\sqrt{5}+3\sqrt{451}$$