210k views
3 votes
If b^2=a then b is what of a?

2 Answers

4 votes
1:: If
a
is divisible by a square of a prime number, then we cannot conclude from |2
a
|
b
2
that |
a
|
b
.

Any time
a
is divisible by a square of a prime number, =⋅
a
=
k

p
n
where ≥2
n

2
and
p
does not divide
k
, you can see that
a
divides (⋅−1)2
(
k

p
n

1
)
2
, but
a
does not divide ⋅−1
k

p
n

1
.

Part 2: If
a
is not divisible by a square of a prime number, then we can conclude from |2
a
|
b
2
that |
a
|
b
.

On the other hand, if
a
is not divisible by a square of a prime number, then =12⋯
a
=
p
1
p
2

p
n
where
p
i
is prime for all
p
. Then, assuming
a
divides 2
b
2
, you can conclude that
p
i
divides 2
b
2
, and therefore
p
i
divides
b
(from prime factorization) for all
i
. From this, you can conclude that
a
divides
b
.
User Breek
by
8.5k points
2 votes

Answer:


\huge\boxed{b = √(a)}

Explanation:

If we have an equation
b^2 = a and we want to find what b is in relation to a, we can change the equation so that we have b on one side and whatever is on the other side is what b is.


b^2 = a

To isolate b, we can take the square root of both sides as taking the square root of something squared results in the base.


√(b^2) = √(a)


b = √(a)

So b is the square root of a.

Hope this helped!

User Dng
by
8.0k points

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