Solve =4(113)-(16)(26)/sqrt{(4(78)-(16)^2)[4(frac{88{28})}-(26)^2}

$$= \frac { 4 ( 113 ) - ( 16 ) ( 26 ) } { \sqrt { ( 4 ( 78 ) - ( 16 ) ^ { 2 } ) [ 4 ( \frac { 88 } { 28 } ) } - ( 26 ) ^ { 2 } }$$

Evaluate

$$\frac{9\sqrt{14}}{7}\approx 4.810702354$$

Solution Steps

Multiply 4 and 113 to get 452.

$$\frac{452-16\times 26}{\sqrt{4\times 78-16^{2}}}$$

Multiply 16 and 26 to get 416.

$$\frac{452-416}{\sqrt{4\times 78-16^{2}}}$$

Subtract 416 from 452 to get 36.

$$\frac{36}{\sqrt{4\times 78-16^{2}}}$$

Multiply 4 and 78 to get 312.

$$\frac{36}{\sqrt{312-16^{2}}}$$

Calculate 16 to the power of 2 and get 256.

$$\frac{36}{\sqrt{312-256}}$$

Subtract 256 from 312 to get 56.

$$\frac{36}{\sqrt{56}}$$

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$\frac{36}{2\sqrt{14}}$$

Rationalize the denominator of \frac{36}{2\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$\frac{36\sqrt{14}}{2\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$\frac{36\sqrt{14}}{2\times 14}$$

Cancel out 2\times 2 in both numerator and denominator.

$$\frac{9\sqrt{14}}{7}$$