Solve 60*2.54divsqrt{(16*16+9*9)}*16

$$60 \times 2.54 \div \sqrt{ (16 \times 16+9 \times 9) } \times 16$$

Evaluate

$$\frac{12192\sqrt{337}}{1685}\approx 132.828111858$$

Solution Steps

Multiply 60 and 2.54 to get 152.4.

$$16\times \frac{152.4}{\sqrt{16\times 16+9\times 9}}$$

Multiply 16 and 16 to get 256. Multiply 9 and 9 to get 81.

$$16\times \frac{152.4}{\sqrt{256+81}}$$

Add 256 and 81 to get 337.

$$16\times \frac{152.4}{\sqrt{337}}$$

Rationalize the denominator of \frac{152.4}{\sqrt{337}} by multiplying numerator and denominator by \sqrt{337}.

$$16\times \frac{152.4\sqrt{337}}{\left(\sqrt{337}\right)^{2}}$$

The square of \sqrt{337} is 337.

$$16\times \frac{152.4\sqrt{337}}{337}$$

Divide 152.4\sqrt{337} by 337 to get \frac{762}{1685}\sqrt{337}.

$$16\times \frac{762}{1685}\sqrt{337}$$

Multiply 16 and \frac{762}{1685} to get \frac{12192}{1685}.

$$\frac{12192}{1685}\sqrt{337}$$