Solve 2^2sqrt{4-2(7)1/4}

$${ 2 }^{ 2 } \sqrt{ 4-2(7) \frac{ 1 }{ 4 } }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$4\sqrt{4-2\times 7\times \frac{1}{4}}$$

Multiply 2 and 7 to get 14.

$$4\sqrt{4-14\times \frac{1}{4}}$$

Multiply 14 and \frac{1}{4} to get \frac{14}{4}.

$$4\sqrt{4-\frac{14}{4}}$$

Reduce the fraction \frac{14}{4} to lowest terms by extracting and canceling out 2.

$$4\sqrt{4-\frac{7}{2}}$$

Convert 4 to fraction \frac{8}{2}.

$$4\sqrt{\frac{8}{2}-\frac{7}{2}}$$

Since \frac{8}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

$$4\sqrt{\frac{8-7}{2}}$$

Subtract 7 from 8 to get 1.

$$4\sqrt{\frac{1}{2}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$4\times \frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$4\times \frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$4\times \frac{\sqrt{2}}{2}$$

Cancel out 2, the greatest common factor in 4 and 2.

$$2\sqrt{2}$$