Solve 2sqrt{28}+2sqrt{28}+sqrt{567}

$$2 \sqrt { 28 } + 2 \sqrt { 28 } + \sqrt { 567 }$$

Evaluate

$$17\sqrt{7}\approx 44.977772288$$

Solution Steps

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}.

$$2\times 2\sqrt{7}+2\sqrt{28}+\sqrt{567}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{7}+2\sqrt{28}+\sqrt{567}$$

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}.

$$4\sqrt{7}+2\times 2\sqrt{7}+\sqrt{567}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{7}+4\sqrt{7}+\sqrt{567}$$

Combine 4\sqrt{7} and 4\sqrt{7} to get 8\sqrt{7}.

$$8\sqrt{7}+\sqrt{567}$$

Factor 567=9^{2}\times 7. Rewrite the square root of the product \sqrt{9^{2}\times 7} as the product of square roots \sqrt{9^{2}}\sqrt{7}. Take the square root of 9^{2}.

$$8\sqrt{7}+9\sqrt{7}$$

Combine 8\sqrt{7} and 9\sqrt{7} to get 17\sqrt{7}.

$$17\sqrt{7}$$