Solve sqrt{(1+4^2)[(1/4)^2-4(-3/4)}]

$$\sqrt { ( 1 + 4 ^ { 2 } ) [ ( \frac { 1 } { 4 } ) ^ { 2 } - 4 ( - \frac { 3 } { 4 } ) } ]$$

Evaluate

$$\frac{7\sqrt{17}}{4}\approx 7.215434845$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\sqrt{\left(1+16\right)\left(\left(\frac{1}{4}\right)^{2}-4\left(-\frac{3}{4}\right)\right)}$$

Add 1 and 16 to get 17.

$$\sqrt{17\left(\left(\frac{1}{4}\right)^{2}-4\left(-\frac{3}{4}\right)\right)}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\sqrt{17\left(\frac{1}{16}-4\left(-\frac{3}{4}\right)\right)}$$

Cancel out 4 and 4.

$$\sqrt{17\left(\frac{1}{16}-\left(-3\right)\right)}$$

The opposite of -3 is 3.

$$\sqrt{17\left(\frac{1}{16}+3\right)}$$

Convert 3 to fraction \frac{48}{16}.

$$\sqrt{17\left(\frac{1}{16}+\frac{48}{16}\right)}$$

Since \frac{1}{16} and \frac{48}{16} have the same denominator, add them by adding their numerators.

$$\sqrt{17\times \frac{1+48}{16}}$$

Add 1 and 48 to get 49.

$$\sqrt{17\times \frac{49}{16}}$$

Express 17\times \frac{49}{16} as a single fraction.

$$\sqrt{\frac{17\times 49}{16}}$$

Multiply 17 and 49 to get 833.

$$\sqrt{\frac{833}{16}}$$

Rewrite the square root of the division \sqrt{\frac{833}{16}} as the division of square roots \frac{\sqrt{833}}{\sqrt{16}}.

$$\frac{\sqrt{833}}{\sqrt{16}}$$

Factor 833=7^{2}\times 17. Rewrite the square root of the product \sqrt{7^{2}\times 17} as the product of square roots \sqrt{7^{2}}\sqrt{17}. Take the square root of 7^{2}.

$$\frac{7\sqrt{17}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\frac{7\sqrt{17}}{4}$$