Solve 9sqrt{5}+10sqrt{45}-10sqrt{125}

$$9 \sqrt { 5 } + 10 \sqrt { 45 } - 10 \sqrt { 125 }$$

Evaluate

$$-11\sqrt{5}\approx -24.596747752$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$9\sqrt{5}+10\times 3\sqrt{5}-10\sqrt{125}$$

Multiply 10 and 3 to get 30.

$$9\sqrt{5}+30\sqrt{5}-10\sqrt{125}$$

Combine 9\sqrt{5} and 30\sqrt{5} to get 39\sqrt{5}.

$$39\sqrt{5}-10\sqrt{125}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$39\sqrt{5}-10\times 5\sqrt{5}$$

Multiply -10 and 5 to get -50.

$$39\sqrt{5}-50\sqrt{5}$$

Combine 39\sqrt{5} and -50\sqrt{5} to get -11\sqrt{5}.

$$-11\sqrt{5}$$