Question

What is equivalent to the square root of -98

Answer 1

`\large\boxed{√(-98)=7\sqrt2\ i}`

Explanation:

`√(-98)=√((-1)(49)(2))\qquad\text{use}\ √(ab)=√(a)\cdot√(b)\\\\=√(-1)\cdot√(49)\cdot\sqrt2\qquad\text{use}\ √(-1)=i\ -\text{an imaginary unit}\\\\=i\cdot7\cdot\sqrt2\qquad√(49)=7\ \text{because}\ 7^2=49\\\\=7\sqrt2\ i`

Answer 2

7√2 i

Explanation:

√(-98)

=√{(-1) .98}

=√(-1 . 2 . 7²)

=√-1 .√2 . √7²

= i . √2 . 7 [∵√-1 = i ]

=7√2 i