Solve 3sqrt{6}+5sqrt{600}

$$3 \sqrt{ 6 } +5 \sqrt{ 600 }$$

Evaluate

$$53\sqrt{6}\approx 129.822956368$$

Solution Steps

Factor 600=10^{2}\times 6. Rewrite the square root of the product \sqrt{10^{2}\times 6} as the product of square roots \sqrt{10^{2}}\sqrt{6}. Take the square root of 10^{2}.

$$3\sqrt{6}+5\times 10\sqrt{6}$$

Multiply 5 and 10 to get 50.

$$3\sqrt{6}+50\sqrt{6}$$

Combine 3\sqrt{6} and 50\sqrt{6} to get 53\sqrt{6}.

$$53\sqrt{6}$$