Math, asked by sairaelsa2312, 11 months ago

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


Anonymous: ___k off

Answers

Answered by CEOEkanshNimbalkar
0

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

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