Solve 128-80/64divsqrt{92}

$$\frac{ 128-80 }{ 64 \div \sqrt{ 92 } }$$

Evaluate

$$\frac{3\sqrt{23}}{2}\approx 7.193747285$$

Solution Steps

Subtract 80 from 128 to get 48.

$$\frac{48}{\frac{64}{\sqrt{92}}}$$

Factor 92=2^{2}\times 23. Rewrite the square root of the product \sqrt{2^{2}\times 23} as the product of square roots \sqrt{2^{2}}\sqrt{23}. Take the square root of 2^{2}.

$$\frac{48}{\frac{64}{2\sqrt{23}}}$$

Rationalize the denominator of \frac{64}{2\sqrt{23}} by multiplying numerator and denominator by \sqrt{23}.

$$\frac{48}{\frac{64\sqrt{23}}{2\left(\sqrt{23}\right)^{2}}}$$

The square of \sqrt{23} is 23.

$$\frac{48}{\frac{64\sqrt{23}}{2\times 23}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{48}{\frac{32\sqrt{23}}{23}}$$

Divide 48 by \frac{32\sqrt{23}}{23} by multiplying 48 by the reciprocal of \frac{32\sqrt{23}}{23}.

$$\frac{48\times 23}{32\sqrt{23}}$$

Cancel out 16 in both numerator and denominator.

$$\frac{3\times 23}{2\sqrt{23}}$$

Rationalize the denominator of \frac{3\times 23}{2\sqrt{23}} by multiplying numerator and denominator by \sqrt{23}.

$$\frac{3\times 23\sqrt{23}}{2\left(\sqrt{23}\right)^{2}}$$

The square of \sqrt{23} is 23.

$$\frac{3\times 23\sqrt{23}}{2\times 23}$$

Multiply 3 and 23 to get 69.

$$\frac{69\sqrt{23}}{2\times 23}$$

Multiply 2 and 23 to get 46.

$$\frac{69\sqrt{23}}{46}$$

Divide 69\sqrt{23} by 46 to get \frac{3}{2}\sqrt{23}.

$$\frac{3}{2}\sqrt{23}$$