Solve 192*2/2sqrt{10000+96*4}

$$\frac { 192 \times 2 } { 2 \sqrt { 10000 + 96 \times 4 } }$$

Evaluate

$$\frac{48\sqrt{649}}{649}\approx 1.884164813$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{2\times 96}{\sqrt{10000+4\times 96}}$$

Multiply 2 and 96 to get 192.

$$\frac{192}{\sqrt{10000+4\times 96}}$$

Multiply 4 and 96 to get 384.

$$\frac{192}{\sqrt{10000+384}}$$

Add 10000 and 384 to get 10384.

$$\frac{192}{\sqrt{10384}}$$

Factor 10384=4^{2}\times 649. Rewrite the square root of the product \sqrt{4^{2}\times 649} as the product of square roots \sqrt{4^{2}}\sqrt{649}. Take the square root of 4^{2}.

$$\frac{192}{4\sqrt{649}}$$

Rationalize the denominator of \frac{192}{4\sqrt{649}} by multiplying numerator and denominator by \sqrt{649}.

$$\frac{192\sqrt{649}}{4\left(\sqrt{649}\right)^{2}}$$

The square of \sqrt{649} is 649.

$$\frac{192\sqrt{649}}{4\times 649}$$

Cancel out 4 in both numerator and denominator.

$$\frac{48\sqrt{649}}{649}$$