Question

What type of number is 4 plus 5 StartRoot 2 EndRoot?

Answer 1

Explanation:

Adding \sqrt{-2}\,\,and\,\,\sqrt{-18}

−2

and

−18

we get 4\sqrt{2i}4

2i

Option C 4 StartRoot 2 EndRoot i is correct.

Explanation:

We need to find the sum of: \sqrt{-2}\,\,and\,\,\sqrt{-18}

−2

and

−18

Finding sum:

\sqrt{-2}+\sqrt{-18}

−2

+

−18

\sqrt{-2}

−2

can be written as \sqrt{2}i

2

i

\sqrt{-18}

−18

can be written as \sqrt{18}i

18

i

We know 18 = 2x3x3 = 2x3^2 so,

\sqrt{2i}+\sqrt{2\times 3^2}i

2i

+

2×3

2

i

\sqrt{2i}+3\sqrt{2}i

2i

+3

2

i

Adding like terms:

4\sqrt{2i}4

2i

So, adding \sqrt{-2}\,\,and\,\,\sqrt{-18}

−2

and

−18

we get 4\sqrt{2i}4

2i

Option C 4 StartRoot 2 EndRoot i is correct.

Keywords: Square root