Solve sqrt{20}xsqrt{30}+1

$$\sqrt { 20 } x \sqrt { 30 } + 1$$

Evaluate

$$10\sqrt{6}x+1$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$2\sqrt{5}x\sqrt{30}+1$$

Factor 30=5\times 6. Rewrite the square root of the product \sqrt{5\times 6} as the product of square roots \sqrt{5}\sqrt{6}.

$$2\sqrt{5}x\sqrt{5}\sqrt{6}+1$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$2\times 5x\sqrt{6}+1$$

Multiply 2 and 5 to get 10.

$$10x\sqrt{6}+1$$

Differentiate w.r.t. x

$$10 \sqrt{6} = 24.494897428$$