Question

How do you simplify sqrt (12) - sqrt (27)?

Answer 1

Step by step explanation :

$\sqrt{12} - \sqrt{27}$

Simplify the radical √12

Factor out the perfect square

$= > \sqrt{2 {}^{2} \times 3 } - \sqrt{27}$

The root of a product is equal to the product of the roots of each factor

$= > \sqrt{2 {}^{2} } \sqrt{3} - \sqrt{27}$

Reduce the index of the radical and exponent with 2

$= > 2 \sqrt{3} - \sqrt{27}$

Simplify the radicle √27. Factor out the perfect square

$= > 2 \sqrt{3} - \sqrt{3 {}^{2} \times 3}$

The root of a product is equal to the product of the roots of each factor.

$= > 2 \sqrt{3} - \sqrt{3 {}^{2} } \sqrt{3}$

Reduce the index of the radical and exponent with 2

$= > 2 \sqrt{3} - 3 \sqrt{3}$

Collect the like terms by subtracting their coefficients.

$= > (2 - 3) \sqrt{3}$

Calculate the difference

$= > - 1 \sqrt{3}$

When the term has a coefficient of - 1, the number doesn't have to be written but the sign remains.

$= > - \sqrt{3}$

$= > - 1.73205$