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mixer [17]
2 years ago
12

Worth 25 points!

Mathematics
1 answer:
MrRissso [65]2 years ago
6 0

Answer:

1) \sqrt{-48}=4\sqrt{3} \ i

2) \sqrt{-63}=3\sqrt{7} \ i

3) \sqrt{-72}=6\sqrt{2} \ i

4) \sqrt{-24}=4\sqrt{6} \ i

5) \sqrt{-84}=2\sqrt{21} \ i

6) \sqrt{-99}=3\sqrt{11} \ i

Step-by-step explanation:

We need to simply the following :

<u>Note: For all questions given we know that </u>\sqrt{-1}=i<u> using it in all the given questions.</u>

1) \sqrt{-48}

Factors of 48 are: 2x2x2x2x3

\sqrt{-48}\\=\sqrt{48}\sqrt{-1}  \\=\sqrt{2\times2\times2\times2\times3}\ i\\=  \sqrt{2^2\times2^2\times3}\ i\\=2\times2\sqrt{3} \ i \\=4\sqrt{3} \ i

2) \sqrt{-63}

Factors of 63 are: 3x3x7

\sqrt{-63}\\=\sqrt{63}\sqrt{-1}  \\=\sqrt{3\times3\times7}\ i\\=  \sqrt{3^2\times7}\ i\\=3\sqrt{7} \ i

3) \sqrt{-72}

Factors of 72 are: 2x2x2x3x3

\sqrt{-72}\\=\sqrt{72}\sqrt{-1}  \\=\sqrt{2\times2\times2\times3\times3}\ i\\=  \sqrt{2^2\times3^2\times2}\ i\\=2\times3\sqrt{2} \ i \\=6\sqrt{2} \ i

4) \sqrt{-24}

Factors of 24 are: 2x2x2x3

\sqrt{-24}\\=\sqrt{24}\sqrt{-1}  \\=\sqrt{2\times2\times2\times3}\ i\\=  \sqrt{2^2\times2\times3}\ i\\=2\sqrt{2\times3} \ i \\=2\sqrt{6} \ i

5) \sqrt{-84}

Factors of 84 are: 2x2x3x7

\sqrt{-84}\\=\sqrt{84}\sqrt{-1}  \\=\sqrt{2\times2\times3\times7}\ i\\=  \sqrt{2^2\times3\times7}\ i\\=2\sqrt{21} \ i

6) \sqrt{-99}\\

Prime factors of 99 are: 3x3x11

\sqrt{-99}\\=\sqrt{99}\sqrt{-1}  \\=\sqrt{3\times3\times11}\ i\\=  \sqrt{3^2\times11}\ i\\=3\sqrt{11} \ i \\=3\sqrt{11} \ i

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