Loading [MathJax]/jax/output/HTML-CSS/jax.js

Arithmetic Sequence Calculator Geometric Sequence Calculator Harmonic Sequence Calculator Fibonacci Sequence Calculator Number Sequence Calculator Sequence Formula Calculator Sum of Linear Number Sequence Calculator Find the sequence and next term Recursive Sequence Calculator First Five Terms of a Sequence Bound Sequence calculator Missing Terms in Arthimetic Sequence calculator Limit of Sequence Calculator Sum of Sequence Calculator Arithemetic Sequence common difference calculator Geometric Sequence Ratio Calculator Arithmetic Sequence Equation Calculator Geometric Sequence Equation Calculator Monotonic Sequence Calculator Partial Sum Arithmetic Sequence Infinite Series Calculator

Simplify ( square root of -125)/( square root of 5)

$\frac{\sqrt{- 125}}{\sqrt{5}}$

Step 1

Pull out imaginary unit

$i$ .

Rewrite

$- 125$ as

$- 1 (125)$ .

$\frac{\sqrt{- 1 (125)}}{\sqrt{5}}$

Rewrite

$\sqrt{- 1 (125)}$ as

$\sqrt{- 1} \cdot \sqrt{125}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{125}}{\sqrt{5}}$

Rewrite

$\sqrt{- 1}$ as

$i$ .

$\frac{i \cdot \sqrt{125}}{\sqrt{5}}$

$\frac{i \cdot \sqrt{125}}{\sqrt{5}}$

Step 2

Combine

$\sqrt{125}$ and

$\sqrt{5}$ into a single radical.

$i \cdot \sqrt{\frac{125}{5}}$

Step 3

Simplify the expression.

Divide

$125$ by

$5$ .

$i \cdot \sqrt{25}$

Rewrite

$25$ as

$5^{2}$ .

$i \cdot \sqrt{5^{2}}$

$i \cdot \sqrt{5^{2}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$i \cdot 5$

Step 5

Move

$5$ to the left of

$i$ .

$5 i$

Related Questions