Solve y:(sqrt{4})(9sqrt{18})

$$y : ( \sqrt { 4 } ) ( 9 \sqrt { 18 } )$$

Evaluate

$$\frac{27\sqrt{2}y}{2}$$

Solution Steps

Calculate the square root of 4 and get 2.

$$\frac{y}{2}\times 9\sqrt{18}$$

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}.

$$\frac{y}{2}\times 9\times 3\sqrt{2}$$

Multiply 9 and 3 to get 27.

$$\frac{y}{2}\times 27\sqrt{2}$$

Express \frac{y}{2}\times 27 as a single fraction.

$$\frac{y\times 27}{2}\sqrt{2}$$

Express \frac{y\times 27}{2}\sqrt{2} as a single fraction.

$$\frac{y\times 27\sqrt{2}}{2}$$

Differentiate w.r.t. y

$$\frac{27 \sqrt{2}}{2} = 19.091883092036785$$