Solve sqrt{28}+5sqrt{63}

$$\sqrt { 28 } + 5 \sqrt { 63 }$$

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}.

$$2\sqrt{7}+5\sqrt{63}$$

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}.

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

Multiply 5 and 3 to get 15.

$$2\sqrt{7}+15\sqrt{7}$$

Combine 2\sqrt{7} and 15\sqrt{7} to get 17\sqrt{7}.

$$17\sqrt{7}$$