Question

√9 = _______
(a) 3
(b) -3
(c) 3 and -3
(d) all a, b, c are true

Answer 1

Solution :

√9 = ± 3

Given all options are wrong .

√9 = 3 or - 3

••••

Answer 2

$\sqrt{9}$



Writting 9 in factors or in simple words splitting 9 in multiplication form.

9 = 1 × 3 × 3 [ whole number ]

9 = 1 × ( - 3 ) × ( - 3 ) { integers }




From above we conclude that the product of two positive 3s and product of two negative 3s is same. therefore



3 × 3 = - 3 × ( - 3 ) -----: ( 1 )



$\sqrt{9} \\ \\ \sqrt{3 \times 3} \\ \\ \sqrt{3 {}^{2} } \\ \\ 3 {}^{2 \times \frac{1}{2} } \\ \\ {3}^{1} \\ \\ 3$



Therefore √9 = 3 ----: ( 2 )




But from ( 1 ) we got that 3 × 3 = - 3 × ( - 3 ) , so substituting the product of - 3s in place of 3s.




$\sqrt{9} \\ \\ \sqrt{3 \times 3} \\ \\ \sqrt{( - 3) \times ( - 3)} \\ \\ \sqrt{( - 3) {}^{2} } \\ \\ ( - 3) {}^{2 \times \frac{1}{2} } \\ \\ ( - 3) {}^{1} \\ \\ - 3$



Therefore , √9 = - 3


From ( ii ) :


√9 = 3 = - 3



But we can't take both the values at same. therefore given all options are wrong.

Option C could be the correct option, if it was 3 or - 3