Solve 0,5*sqrt{40}+3*sqrt{90}=

$$0,5 \cdot \sqrt { 40 } + 3 \cdot \sqrt { 90 } =$$

Evaluate

$$10\sqrt{10}\approx 31.622776602$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$0,5\times 2\sqrt{10}+3\sqrt{90}$$

Multiply 0,5 and 2 to get 1.

$$\sqrt{10}+3\sqrt{90}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$\sqrt{10}+3\times 3\sqrt{10}$$

Multiply 3 and 3 to get 9.

$$\sqrt{10}+9\sqrt{10}$$

Combine \sqrt{10} and 9\sqrt{10} to get 10\sqrt{10}.

$$10\sqrt{10}$$