Solve frac{isqrt{5}}{isqrt{1/5}}

$$\frac { i \sqrt { 5 } } { i \sqrt { \frac { 1 } { 5 } } }$$

Evaluate

$$5$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\sqrt{5}}{\sqrt{\frac{1}{5}}i^{0}}$$

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$\frac{\sqrt{5}}{\frac{\sqrt{1}}{\sqrt{5}}i^{0}}$$

Calculate the square root of 1 and get 1.

$$\frac{\sqrt{5}}{\frac{1}{\sqrt{5}}i^{0}}$$

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}i^{0}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{\frac{\sqrt{5}}{5}i^{0}}$$

Calculate i to the power of 0 and get 1.

$$\frac{\sqrt{5}}{\frac{\sqrt{5}}{5}\times 1}$$

Express \frac{\sqrt{5}}{5}\times 1 as a single fraction.

$$\frac{\sqrt{5}}{\frac{\sqrt{5}}{5}}$$

Divide \sqrt{5} by \frac{\sqrt{5}}{5} by multiplying \sqrt{5} by the reciprocal of \frac{\sqrt{5}}{5}.

$$\frac{\sqrt{5}\times 5}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{5}\times 5}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}\times 5\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}\times 5\sqrt{5}}{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{5\times 5}{5}$$

Multiply 5 and 5 to get 25.

$$\frac{25}{5}$$

Divide 25 by 5 to get 5.

$$5$$

Real Part

$$5$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$Re(\frac{\sqrt{5}}{\sqrt{\frac{1}{5}}i^{0}})$$

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$Re(\frac{\sqrt{5}}{\frac{\sqrt{1}}{\sqrt{5}}i^{0}})$$

Calculate the square root of 1 and get 1.

$$Re(\frac{\sqrt{5}}{\frac{1}{\sqrt{5}}i^{0}})$$

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$Re(\frac{\sqrt{5}}{\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}i^{0}})$$

The square of \sqrt{5} is 5.

$$Re(\frac{\sqrt{5}}{\frac{\sqrt{5}}{5}i^{0}})$$

Calculate i to the power of 0 and get 1.

$$Re(\frac{\sqrt{5}}{\frac{\sqrt{5}}{5}\times 1})$$

Express \frac{\sqrt{5}}{5}\times 1 as a single fraction.

$$Re(\frac{\sqrt{5}}{\frac{\sqrt{5}}{5}})$$

Divide \sqrt{5} by \frac{\sqrt{5}}{5} by multiplying \sqrt{5} by the reciprocal of \frac{\sqrt{5}}{5}.

$$Re(\frac{\sqrt{5}\times 5}{\sqrt{5}})$$

Rationalize the denominator of \frac{\sqrt{5}\times 5}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$Re(\frac{\sqrt{5}\times 5\sqrt{5}}{\left(\sqrt{5}\right)^{2}})$$

The square of \sqrt{5} is 5.

$$Re(\frac{\sqrt{5}\times 5\sqrt{5}}{5})$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$Re(\frac{5\times 5}{5})$$

Multiply 5 and 5 to get 25.

$$Re(\frac{25}{5})$$

Divide 25 by 5 to get 5.

$$Re(5)$$

The real part of 5 is 5.

$$5$$