Solve sqrt{7}+2sqrt{63}+4sqrt{28}

$$\sqrt { 7 } + 2 \sqrt { 63 } + 4 \sqrt { 28 }$$

Evaluate

$$15\sqrt{7}\approx 39.686269666$$

Solution Steps

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$\sqrt{7}+2\times 3\sqrt{7}+4\sqrt{28}$$

Multiply 2 and 3 to get 6.

$$\sqrt{7}+6\sqrt{7}+4\sqrt{28}$$

Combine \sqrt{7} and 6\sqrt{7} to get 7\sqrt{7}.

$$7\sqrt{7}+4\sqrt{28}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$7\sqrt{7}+4\times 2\sqrt{7}$$

Multiply 4 and 2 to get 8.

$$7\sqrt{7}+8\sqrt{7}$$

Combine 7\sqrt{7} and 8\sqrt{7} to get 15\sqrt{7}.

$$15\sqrt{7}$$