Solve -25sqrt{180}+35sqrt{360}

$$- 25 \sqrt { 180 } + 35 \sqrt { 360 }$$

Evaluate

$$210\sqrt{10}-150\sqrt{5}\approx 328.66811201$$

Solution Steps

Factor 180=6^{2}\times 5. Rewrite the square root of the product \sqrt{6^{2}\times 5} as the product of square roots \sqrt{6^{2}}\sqrt{5}. Take the square root of 6^{2}.

$$-25\times 6\sqrt{5}+35\sqrt{360}$$

Multiply -25 and 6 to get -150.

$$-150\sqrt{5}+35\sqrt{360}$$

Factor 360=6^{2}\times 10. Rewrite the square root of the product \sqrt{6^{2}\times 10} as the product of square roots \sqrt{6^{2}}\sqrt{10}. Take the square root of 6^{2}.

$$-150\sqrt{5}+35\times 6\sqrt{10}$$

Multiply 35 and 6 to get 210.

$$-150\sqrt{5}+210\sqrt{10}$$

Factor

$$30 {(7 \sqrt{10} - 5 \sqrt{5})} = 328.66811201$$