Solve 3sqrt{18}y-3/4ysqrt{32}

$$3 \sqrt { 18 } y - \frac { 3 } { 4 } y \sqrt { 32 }$$

Evaluate

$$6\sqrt{2}y$$

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}.

$$3\times 3\sqrt{2}y-\frac{3}{4}y\sqrt{32}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{2}y-\frac{3}{4}y\sqrt{32}$$

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}.

$$9\sqrt{2}y-\frac{3}{4}y\times 4\sqrt{2}$$

Cancel out 4 and 4.

$$9\sqrt{2}y-3y\sqrt{2}$$

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

$$6\sqrt{2}y$$

Differentiate w.r.t. y

$$6 \sqrt{2} = 8.485281374$$