Question

If b^2=a then b is what of a?

Answer 1

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
.

Answer 2

Answer:

$\huge\boxed{b = \sqrt{a}}$

Step-by-step 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.

$\sqrt{b^2} = \sqrt{a}$

$b = \sqrt{a}$

So b is the square root of a.

Hope this helped!