Simpify The square root of -144

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durbanville's profile pic

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

The first thing to do is to convert the negative so that we can find the square root of 144

`therefore sqrt(-144) = sqrt(-1 times 144)`

As `sqrt(-1) = i`

`therefore sqrt(-144) = isqrt(144)`

144 is a square number (12 x 12) 

`therefore = i sqrt(12 times 12)`  Note:`sqrt(12 times 12) = 12`  

`therefore = 12 i`

Ans: The square root of -144 = 12i

aruv's profile pic

aruv | High School Teacher | (Level 2) Valedictorian

Posted on

Let number be x ,whose square be -144 i.e.

`x^2=-144=-1xx144=i^2xx144` ,where  `i^2=-1`

`x^2=i^2xx2xx2xx2xx2xx3xx3`

`x=sqrt(i^2xx2xx2xx2xx2xx3xx3)`

`x=+-ixx2xx2xx3`

`x=+-i12`

taangerine's profile pic

taangerine | Student, Grade 12 | (Level 1) Valedictorian

Posted on

Since it is negative, there will be an i in the answer. 144 is a perfect square for 12. Therefore the answer is -12. 

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

the square root of 144 is 12 but because it is -144 the 12 will have to be a complex number therefore imaginary.

so `sqrt(-144)=12i`

zumba96's profile pic

zumba96 | Student, Grade 11 | (Level 3) Valedictorian

Posted on

The square root of -144

`sqrt(-144)=sqrt((-1)(144))`

`sqrt(144)i`

`sqrt(12i)`

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