Solve 661/sqrt{288}

$$\frac{ 661 }{ \sqrt{ 288 } }$$

Evaluate

$$\frac{661\sqrt{2}}{24}\approx 38.94979853$$

Solution Steps

Factor 288=12^{2}\times 2. Rewrite the square root of the product \sqrt{12^{2}\times 2} as the product of square roots \sqrt{12^{2}}\sqrt{2}. Take the square root of 12^{2}.

$$\frac{661}{12\sqrt{2}}$$

Rationalize the denominator of \frac{661}{12\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{661\sqrt{2}}{12\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{661\sqrt{2}}{12\times 2}$$

Multiply 12 and 2 to get 24.

$$\frac{661\sqrt{2}}{24}$$