Verified answer

When you multiply 2 square roots, you multiply the numbers under the radicals, and put them under one radical, so,

√12 × √3 = √36

We use this principle to simplify square roots by breaking up numbers and factoring our perfect squares, so for the example you provided, we can break up the original square root:

√12x^2 = √4 × √3 × √x^2 (since 4 × 3 × x^2 = 12x^2, and 4 and x^2 are perfect squares)

√4 = 2

√x^2 = x

√3 = √3 since it is an irrational number, it remains unchanged.

2x√3 is the result of putting everything back together.

Squrt(12x^2)=

Squrt(4*3*x*x)=

Squrt(2*2*3*x*x)

there are 2 2's and 2 x's inside the radical, so pull the set out

2x squurt(3)

AS GIVEN question MUST be read as :-

√(12) x² = (2√3) x²

However I suspect that what you actually mean is :-

√ (12 x²) = √12 x = 2√3 x

2X √ 3

SOLUTION:

Factor the radicand in such a way that one of the factor is a perfect square

√(4)(3)(x^2)

extract the root of perfect square factor

2x √ 3

sqrt(12x^2)

= sqrt(4 * 3 * x^2)

= sqrt(4) * sqrt(3) * sqrt(x^2)

= 2 * sqrt(3) * |x|

= 2|x|*sqrt(3)

NOTE: 2x*sqrt(3) is correct ONLY if x >= 0

√12x^2

2x√3

(2.2.3.x.x)^1/2

=2x(3)1/2