Solve sqrt{45*28}sqrt{7269}x86/66

$$\sqrt{ 45 \cdot 28 } \sqrt{ 7269 } x \frac{ 86 }{ 66 }$$

Evaluate

$$\frac{86\sqrt{254415}x}{11}$$

Solution Steps

Multiply 45 and 28 to get 1260.

$$\sqrt{1260}\sqrt{7269}x\times \frac{86}{66}$$

Factor 1260=6^{2}\times 35. Rewrite the square root of the product \sqrt{6^{2}\times 35} as the product of square roots \sqrt{6^{2}}\sqrt{35}. Take the square root of 6^{2}.

$$6\sqrt{35}\sqrt{7269}x\times \frac{86}{66}$$

Reduce the fraction \frac{86}{66} to lowest terms by extracting and canceling out 2.

$$6\sqrt{35}\sqrt{7269}x\times \frac{43}{33}$$

Express 6\times \frac{43}{33} as a single fraction.

$$\frac{6\times 43}{33}\sqrt{35}\sqrt{7269}x$$

Multiply 6 and 43 to get 258.

$$\frac{258}{33}\sqrt{35}\sqrt{7269}x$$

Reduce the fraction \frac{258}{33} to lowest terms by extracting and canceling out 3.

$$\frac{86}{11}\sqrt{35}\sqrt{7269}x$$

To multiply \sqrt{35} and \sqrt{7269}, multiply the numbers under the square root.

$$\frac{86}{11}\sqrt{254415}x$$

Differentiate w.r.t. x

$$\frac{86 \sqrt{254415}}{11} = 3943.457119024724$$