Solve 3sqrt{54}-3sqrt{16}-3sqrt{250}

$$3 \sqrt{ 54 } -3 \sqrt{ 16 } -3 \sqrt{ 250 }$$

Evaluate

$$9\sqrt{6}-15\sqrt{10}-12\approx -37.388757217$$

Solution Steps

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$3\times 3\sqrt{6}-3\sqrt{16}-3\sqrt{250}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{6}-3\sqrt{16}-3\sqrt{250}$$

Calculate the square root of 16 and get 4.

$$9\sqrt{6}-3\times 4-3\sqrt{250}$$

Multiply -3 and 4 to get -12.

$$9\sqrt{6}-12-3\sqrt{250}$$

Factor 250=5^{2}\times 10. Rewrite the square root of the product \sqrt{5^{2}\times 10} as the product of square roots \sqrt{5^{2}}\sqrt{10}. Take the square root of 5^{2}.

$$9\sqrt{6}-12-3\times 5\sqrt{10}$$

Multiply -3 and 5 to get -15.

$$9\sqrt{6}-12-15\sqrt{10}$$

Factor

$$3 {(3 \sqrt{6} - 5 \sqrt{10} - 4)} = -37.388757217$$