Why we can square both sides of an equation that have square root at both of the equation side?

Question

Why we can square both sides of an equation that have square root at both of the equation side?

Answer 1

The reason is that squaring a value is the same process as multiplying that value times itself. If the two original values are equal, their squares will be equal as well.

Answer 2

since sqrt  is just  1/2  in exponent form

  

Answer 3

it is possible because it does not change the final value of the equation.

Squaring both the sides is just as similar as multiplying any number x (say 2) to both the sides of the equation.

Example :

i have an equation

2x² = 8

{in this the value of x becomes 2}

if I multiply the equation by 5 [on both sides]

the equation becomes

10x² = 40

Here too the value of x remains the same i.e 4

Answer 4

You can do it even if there aren't square roots involved,

but then it might not be as useful.

It's a special case of "equals multiplied by equals remain equal".

If we have x = y, then ax = ay for any a.

Since x = y, we can substitute x for a on the left

and y for a on the right, and end up with

x² = y².

=

Answer 5

You can do anything with both sides.

Answer 6

by exemple:

square root (x) = x^1/2

(x^1/2)^2 = x^(1/2 x 2) = x

[square root (x)]^2 = (x^1/2)^2 = x

If it is:

square root (x-2) = square root (2x +1)

you can square both sides to get the roots off so that it is obtained the same solution, it is said, the same solution that:

x - 2 = 2x + 1

which is easier to solve.