Solve .915-1.6450.007/sqrt{32}

$$.915-1.645 \frac{ 0.007 }{ \sqrt{ 32 } }$$

Evaluate

$$-\frac{2303\sqrt{2}}{1600000}+0.915\approx 0.912964416$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$0.915-1.645\times \frac{0.007}{4\sqrt{2}}$$

Rationalize the denominator of \frac{0.007}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$0.915-1.645\times \frac{0.007\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$0.915-1.645\times \frac{0.007\sqrt{2}}{4\times 2}$$

Multiply 4 and 2 to get 8.

$$0.915-1.645\times \frac{0.007\sqrt{2}}{8}$$

Divide 0.007\sqrt{2} by 8 to get 0.000875\sqrt{2}.

$$0.915-1.645\times 0.000875\sqrt{2}$$

Multiply 1.645 and 0.000875 to get 0.001439375.

$$0.915-0.001439375\sqrt{2}$$