Solve sqrt{20}+sqrt{18}-5sqrt{8}+sqrt{48}2sqrt{45}

$$\sqrt { 20 } + \sqrt { 18 } - 5 \sqrt { 8 } + \sqrt { 48 } 2 \sqrt { 45 }$$

Evaluate

$$2\sqrt{5}+24\sqrt{15}-7\sqrt{2}\approx 87.524241327$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$2\sqrt{5}+\sqrt{18}-5\sqrt{8}+2\sqrt{48}\sqrt{45}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$2\sqrt{5}+3\sqrt{2}-5\sqrt{8}+2\sqrt{48}\sqrt{45}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{5}+3\sqrt{2}-5\times 2\sqrt{2}+2\sqrt{48}\sqrt{45}$$

Multiply -5 and 2 to get -10.

$$2\sqrt{5}+3\sqrt{2}-10\sqrt{2}+2\sqrt{48}\sqrt{45}$$

Combine 3\sqrt{2} and -10\sqrt{2} to get -7\sqrt{2}.

$$2\sqrt{5}-7\sqrt{2}+2\sqrt{48}\sqrt{45}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$2\sqrt{5}-7\sqrt{2}+2\times 4\sqrt{3}\sqrt{45}$$

Multiply 2 and 4 to get 8.

$$2\sqrt{5}-7\sqrt{2}+8\sqrt{3}\sqrt{45}$$

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}.

$$2\sqrt{5}-7\sqrt{2}+8\sqrt{3}\times 3\sqrt{5}$$

Multiply 8 and 3 to get 24.

$$2\sqrt{5}-7\sqrt{2}+24\sqrt{3}\sqrt{5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$2\sqrt{5}-7\sqrt{2}+24\sqrt{15}$$