express each number in terms of i, and simplify?

Question

1. 3 square root of -11.
2. 4 square root of - 49/64
3. (3/5) square root of -100/9
4. - square root of -10
5. - square root of -28
6. 2 square root of -75
7. 5 square root of -8
8. 2/3 square root of -72
9. - 1/2 square root of -72
10. -1/2 square root of -300
11. - square -1/3
12. 4 square root of -1/8
13. square root of -0.72

Answer 1

What we'll be using here is the fact that

√(-1) = i

and so √(-2) = i√2, √(-3) = i√3, √(-4) = i√4 = 2i etc.

1.) 3√(-11) = 3i√11
2.) 4√(-49/64) = 4i√49/√64 = 4·i·7 / 8 = 7i/2
3.) 3/5 √(-100/9) = 3/5 · i · √100/√9 = 3/5 · i · 10/3 = 2i
4.) -√(-10) = -i√10
5.) - √(-28) = -i√28 = -i√(4·7) = -i√4·√7 = -2i√7
6.) 2√(-75) = 2i√75 = 2i√(25·3) = 2i√25·√3 = 10i√3
7.) 5√(-8) = 5i√(4·2) = 10i√2
8.) 2/3√(-72) = 2/3 · i · √(36·2) = 2/3 · i · 6 · √2 = 4i√2
9.) -1/2√(-72) = -1/2· i · 6 · √2 = -3i√2
10.) -1/2√(-300) = -1/2· i · √(100·3) = -1/2· i · 10 · √3 = -5i√3
11.) - √(-1/3) = - i √(1/3) = - i √1/√3 = -i/√3
12.) 4√(-1/8) = 4i √1/√8 = 4i/√8 = 4i/√(4·2) = 4i/2√2 = 2i/√2
13.) √(-0.72) = i·√0.72 = i·√(72/100) = i·6 ·√2 / 10 = 3i√2 / 5

The answers to questions 11 and 12 can also be further simplified - we can rationalize these fractions (so that there are no square roots in the denominator). We do that by multiplying top and bottom of the fraction by the appropriate square root:
-i/√3 = (-i · √3) / (√3 · √3) = -i√3/3
2i/√2 = (2i · √2) / (√2 · √2) = 2i·√2 / 2 = i√2

Hope this helps.

Answer 2

1. 3i√11
2. 7i/2
3. 2i
4. -i√10
5. -2i√7
6. 10i√3
7.10i√2
8. 4i√2
9. -3i√2
10. -5i√3
11. (-i√3)/3
12. i√2
13. (3i√2)/5

Answer 3

use a clinical calculator? sort the quantity in and press s/d some circumstances till you get it :p in case you like it on paper its some thing like: 0.11.. = 1x a million.11.. = 10x 11.11.. = 100x 100x - 1x = 99x (11) answer = 11/ninety 9

Answer 4

1. 3 square root of -11.=3 sq.rt.11 times i
2. 4 square root of - 49/64 =(7/2) i
3. (3/5) square root of -100/9 =2i
4. - square root of -10=-sq.rt.10 times i
5. - square root of -28=-2 sq.rt.7 times i
6. 2 square root of -75=10 sq.rt.2 times i
7. 5 square root of -8=10 sq.rt.2 times i
8. 2/3 square root of -72=4 sq.rt 2 times i
9. - 1/2 square root of -72=-3 sq.rt.2 times i
10. -1/2 square root of -300=-5 sq.rt.3 times i
11. - square -1/3=-[(sq.rt.3)/3]times i
12. 4 square root of -1/8=sq.rt.2 times i
13. square root of -0.72 =0.6sq.rt.2 times i

Answer 5

basic ideal i=imaginary i^2=-1

Answer 6

3√- 11 =

3i√11

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