Question

MathaMagics™ V¹ : What is the value of √9 ? , Prove your answer .
NOTE : kindly research before answering because wrong answer will be reported .

Answer 1

Hey ,

OK , so everyone says √9 = +(-)3
and teachers told us too , so it must be right ?
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No , it's not.
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The value of √9 is actually just +3.
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Why ?.
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OK , let's take a number , um.. 2
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now , 2¹ = 2
2² = 4
2³ = 8
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and so on , we notice that along with the power the number keeps increasing .
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now what do I do to decrease the number ?
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should I decrease the power towards 0
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.OK
2½ = √2
2⅓ = ³√2
and so on .
if u notice the number starts to decrease .. but it won't even go down to zero or negativity.
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now , should I try negative powers ?
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1\2¹ = 1\2
1\2² = 1\4
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now too the number keeps decreasing but never goes down to zero or negativity .

Overall there is nothing taken as a power by which we can make a number exact zero or make it negative .

then how can we say that 9½ = -3 ?
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get it ?
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now u will say that is ( -3 )² = 9 also wrong ?
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when did I say that its wrong ?
its correct but not vice versa.
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Overall , the value of √x is always positive for x belong to natural numbers .
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and value of √9 is always +3 .

HENCE PROVED.

Answer 2

this can be proved by calculus ,

here we can see the graph of y = √x .
this is always positive , but why ????

reason :-
let a number is x²
we find its square root
e.g √x² = | x |

but we know , modulus function is want to positive
y = | x |
if x >0 then, y = x

if x < 0 then, y = -x

now,
for, y = √9

similarly y = | 3 |

but 3 > 0 so, y = 3

you can also see the graph of square root .

value will be ony positive of square root function ,

hence, √9 = 3