Best solutions to - "Evaluate the radical expression, and express the result..."

Lipossig

Answered question

2021-09-06

Evaluate the radical expression, and express the result in the form a + bi.

\frac{2 + \sqrt{- 8}}{1 + \sqrt{- 2}}

averes8

Skilled2021-09-07Added 92 answers

The value of the imaginary number i is equal to

\sqrt{- 1}

and

i^{2} = - 1

Substitute i for

\sqrt{- 1}

in the radical expression.

\frac{2 + \sqrt{- 8}}{1 + \sqrt{- 2}} = \frac{2 + i \sqrt{8}}{1 + i \sqrt{2}}

Multiply the numerator and the denominator of the radical expression with the conjugate of the denominator, that is,

1 - i \sqrt{2}

and simplify as follows:

\frac{2 + i \sqrt{8}}{1 + i \sqrt{2}} = \frac{2 + i \sqrt{8}}{1 + i \sqrt{2}} \times \frac{1 - i \sqrt{2}}{1 - i \sqrt{2}}

= \frac{2 - 2 i \sqrt{2} + i \sqrt{8} - i^{2} \sqrt{8} \sqrt{2}}{i^{2} - {(i \sqrt{2})}^{2}}

= \frac{2 - 2 i \sqrt{2} + 2 i \sqrt{2} - (- 1) \sqrt{16}}{1 - (- 1) (2)}

= \frac{2 + 4}{1 + 2}

= \frac{6}{3}

= 2 + 0 i

Therefore,

\frac{2 + \sqrt{- 8}}{1 + \sqrt{- 2}} = 2 + 0 i

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?