Solve 4sqrt{63}+sqrt{28}+16sqrt{7}

$$4 \sqrt { 63 } + \sqrt { 28 } + 16 \sqrt { 7 }$$

Evaluate

$$30\sqrt{7}\approx 79.372539332$$

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}.

$$4\times 3\sqrt{7}+\sqrt{28}+16\sqrt{7}$$

Multiply 4 and 3 to get 12.

$$12\sqrt{7}+\sqrt{28}+16\sqrt{7}$$

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}.

$$12\sqrt{7}+2\sqrt{7}+16\sqrt{7}$$

Combine 12\sqrt{7} and 2\sqrt{7} to get 14\sqrt{7}.

$$14\sqrt{7}+16\sqrt{7}$$

Combine 14\sqrt{7} and 16\sqrt{7} to get 30\sqrt{7}.

$$30\sqrt{7}$$