Solve 45420+1.962050/sqrt{256}

$$45420 + 1.96 \frac { 2050 } { \sqrt { 256 } }$$

Evaluate

$$45671.125$$

Solution Steps

Calculate the square root of 256 and get 16.

$$45420+1.96\times \frac{2050}{16}$$

Reduce the fraction \frac{2050}{16} to lowest terms by extracting and canceling out 2.

$$45420+1.96\times \frac{1025}{8}$$

Convert decimal number 1.96 to fraction \frac{196}{100}. Reduce the fraction \frac{196}{100} to lowest terms by extracting and canceling out 4.

$$45420+\frac{49}{25}\times \frac{1025}{8}$$

Multiply \frac{49}{25} times \frac{1025}{8} by multiplying numerator times numerator and denominator times denominator.

$$45420+\frac{49\times 1025}{25\times 8}$$

Do the multiplications in the fraction \frac{49\times 1025}{25\times 8}.

$$45420+\frac{50225}{200}$$

Reduce the fraction \frac{50225}{200} to lowest terms by extracting and canceling out 25.

$$45420+\frac{2009}{8}$$

Convert 45420 to fraction \frac{363360}{8}.

$$\frac{363360}{8}+\frac{2009}{8}$$

Since \frac{363360}{8} and \frac{2009}{8} have the same denominator, add them by adding their numerators.

$$\frac{363360+2009}{8}$$

Add 363360 and 2009 to get 365369.

$$\frac{365369}{8}$$

Factor

$$\frac{365369}{2 ^ {3}} = 45671\frac{1}{8} = 45671.125$$