Solve sqrt{18}+3sqrt{8}+3sqrt{32}-sqrt{60}

$$\sqrt { 18 } + 3 \sqrt { 8 } + 3 \sqrt { 32 } - \sqrt { 60 }$$

Evaluate

$$21\sqrt{2}-2\sqrt{15}\approx 21.952518117$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$3\sqrt{2}+3\sqrt{8}+3\sqrt{32}-\sqrt{60}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$3\sqrt{2}+3\times 2\sqrt{2}+3\sqrt{32}-\sqrt{60}$$

Multiply 3 and 2 to get 6.

$$3\sqrt{2}+6\sqrt{2}+3\sqrt{32}-\sqrt{60}$$

Combine 3\sqrt{2} and 6\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}+3\sqrt{32}-\sqrt{60}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$9\sqrt{2}+3\times 4\sqrt{2}-\sqrt{60}$$

Multiply 3 and 4 to get 12.

$$9\sqrt{2}+12\sqrt{2}-\sqrt{60}$$

Combine 9\sqrt{2} and 12\sqrt{2} to get 21\sqrt{2}.

$$21\sqrt{2}-\sqrt{60}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$21\sqrt{2}-2\sqrt{15}$$