1) ![\sqrt{-48}=4\sqrt{3} \ i](/tpl/images/0938/7583/8a618.png)
2) ![\sqrt{-63}=3\sqrt{7} \ i](/tpl/images/0938/7583/11e1f.png)
3) ![\sqrt{-72}=6\sqrt{2} \ i](/tpl/images/0938/7583/80cd9.png)
4) ![\sqrt{-24}=4\sqrt{6} \ i](/tpl/images/0938/7583/f35d9.png)
5) ![\sqrt{-84}=2\sqrt{21} \ i](/tpl/images/0938/7583/392ad.png)
6) ![\sqrt{-99}=3\sqrt{11} \ i](/tpl/images/0938/7583/3492c.png)
Step-by-step explanation:
We need to simply the following :
Note: For all questions given we know that
using it in all the given questions.
1) ![\sqrt{-48}](/tpl/images/0938/7583/5fbba.png)
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](/tpl/images/0938/7583/e5089.png)
2) ![\sqrt{-63}](/tpl/images/0938/7583/4d2d5.png)
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](/tpl/images/0938/7583/229be.png)
3) ![\sqrt{-72}](/tpl/images/0938/7583/ccfeb.png)
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](/tpl/images/0938/7583/423ce.png)
4) ![\sqrt{-24}](/tpl/images/0938/7583/17a64.png)
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](/tpl/images/0938/7583/e8d1a.png)
5) ![\sqrt{-84}](/tpl/images/0938/7583/558ae.png)
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](/tpl/images/0938/7583/80c2a.png)
6) ![\sqrt{-99}\\](/tpl/images/0938/7583/8962f.png)
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](/tpl/images/0938/7583/3ce6c.png)