Solve 8sqrt{18}+10sqrt{60}

$$8 \sqrt { 18 } + 10 \sqrt { 60 }$$

Evaluate

$$20\sqrt{15}+24\sqrt{2}\approx 111.400792421$$

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}.

$$8\times 3\sqrt{2}+10\sqrt{60}$$

Multiply 8 and 3 to get 24.

$$24\sqrt{2}+10\sqrt{60}$$

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}.

$$24\sqrt{2}+10\times 2\sqrt{15}$$

Multiply 10 and 2 to get 20.

$$24\sqrt{2}+20\sqrt{15}$$

Factor

$$4 {(5 \sqrt{15} + 6 \sqrt{2})} = 111.400792421$$