Question

What are the square roots of; (note: i think there are supposed to be 2 each) 36 12 1.96 0.64 400 25/36

Answer 1

36 : 6 and -6

12 =
`2√(3) , -2√(3)`

1.96 =1.4 and -1.4

0.64 : 0.8 and -0.8

400 : 20 and -20

25/36 = 5/6 and -5/6

Explanation:

we know that

(-x)^2 = x^2

ALSO

(x)^2 = x^2

thus, square of both negative and positive number is same positive number.

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36 = 6*6

36 = -6*-6

hence

square roots of 36 is both -6 and 6

12 = 4*3 =
`2^2*√(3) *√(3)`

`√(12) = 2√(3)`

also

12 =
`-2√(3) *-2√(3)`

`√(12) = -2√(3)`

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1.96 = 196/100 = (14/10)^2

1.96 = 196/100 = (-14/10)^2

hence

`√(1.96) = 14/10 \ or -14/10`

_______________________________

0.64 = 64/100 = (8/10)^2 = 0.8^2

0.64 = 64/100 = (-8/10)^2 = (-0.8)^2

Thus, square root of 0.64 = 0.8 and -0.8

_________________________________

400 = 20^2

400 = (-20)^2

`√(400) = 20\\√(400) = -20\\`

__________________________________

25/36 = (5/6)^2

25/36 = (-5/6)^2

`√( 25/36) = 5/6 \\√( 25/36) = (-5/6`