Question

Simplify each square root:

1. square root of -25
2. square root of 1.44
3. square root of + or -16/49
4. square root of 361
5. square root of 49
6. square root of + or -0.64
7. square root of -6.25
8. square root of 169/196
9. square root of 25/324

Answer 1

`1.\ √(-25)-isn't\ real\ number\to√(-25)=√(25(-1))=√(25)\cdot√(-1)=5i\\\\2.\ √(1.44)=√(1.2^2)=1.2\\\\3.\ \sqrt{(16)/(49)}=(√(16))/(√(49))=(√(4^2))/(√(7^2))=(4)/(7)\\\\\sqrt{-(16)/(49)}=(4)/(7)i\\\\4.\ √(361)=√(19^2)=19\\\\5.\ √(49)=√(7^2)=7\\\\6.\ √(0.64)=√(0.8^2)=0.8\\\\√(-0.64)=0.8i`


`7.\ √(-6.25)=√(6.25(-1))=√(6.25)\cdot√(-1)=√(2.5^2)\cdot\sqty{-1}=2.5i\\\\8.\ \sqrt(169)/(196)=(√(169))/(√(196))=(√(13^2))/(√(14^2))=(13)/(14)\\\\9.\ \sqrt(25)/(324)=(√(25))/(√(324))=(√(5^2))/(√(18^2))=(5)/(18)\\====================================`


`i=√(-1)\ is\ the\ imaginary\ unit\\---------------------\\If\ a\geq0\ then\ √(a^2)=a`