Solve 5sqrt{2}+2sqrt{30}+2sqrt{30}+2sqrt{72}

$$5 \sqrt{ 2 } +2 \sqrt{ 30 } +2 \sqrt{ 30 } +2 \sqrt{ 72 }$$

Evaluate

$$4\sqrt{30}+17\sqrt{2}\approx 45.950532861$$

Solution Steps

Combine 2\sqrt{30} and 2\sqrt{30} to get 4\sqrt{30}.

$$5\sqrt{2}+4\sqrt{30}+2\sqrt{72}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$5\sqrt{2}+4\sqrt{30}+2\times 6\sqrt{2}$$

Multiply 2 and 6 to get 12.

$$5\sqrt{2}+4\sqrt{30}+12\sqrt{2}$$

Combine 5\sqrt{2} and 12\sqrt{2} to get 17\sqrt{2}.

$$17\sqrt{2}+4\sqrt{30}$$

Factor

$$4 \sqrt{30} + 17 \sqrt{2} = 45.950532861$$