Solve sqrt{3}(3sqrt{15}-7sqrt{3})

$$\sqrt { 3 } ( 3 \sqrt { 15 } - 7 \sqrt { 3 } )$$

Evaluate

$$9\sqrt{5}-21\approx -0.875388203$$

Solution Steps

Use the distributive property to multiply \sqrt{3} by 3\sqrt{15}-7\sqrt{3}.

$$3\sqrt{3}\sqrt{15}-7\left(\sqrt{3}\right)^{2}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$3\sqrt{3}\sqrt{3}\sqrt{5}-7\left(\sqrt{3}\right)^{2}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$3\times 3\sqrt{5}-7\left(\sqrt{3}\right)^{2}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{5}-7\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$9\sqrt{5}-7\times 3$$

Multiply -7 and 3 to get -21.

$$9\sqrt{5}-21$$

Factor

$$3 {(3 \sqrt{5} - 7)} = -0.875388203$$