To calculate: The simplified form of the expression displaystylefrac{sqrt{{12}}}{sqrt{{{x}+{1}}}}.

Wribreeminsl 2020-12-16 Answered
To calculate: The simplified form of the expression 12x+1.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

gwibdaithq
Answered 2020-12-17 Author has 84 answers

Formula used:
Product property of radicals: anbn=abn
Power property of radicals: (am)n=amn
Calculation:
Consider the provided expression, 12x+1
Multiply numerator and denominator by x+1 so that the radicand in the denominator is a perfect square.
Therefore,
12x+1=12x+1x+1x+1
Here, x>1
Apply the product property of radicals:
anbn=abn
Therefore,
12x+1=43x+1(x+1)(x+1)
=32x+1(x+1)2
Apply power property (am)n=amn in expression (x+1)2.
Therefore,
(x+1)2=((x+1)2)12
=(x+1)212
=(x+1)1
=(x+1)
Therefore,
12x+1=32x+1x+1
Apply the product property of radicals: anbn=abn in the numerator,
3x+1=3(x+1)
=3x+3
Hence,
12x+1=3x+32x+1
Therefore, the simplified form of the expression 12x+1 is 3x+32x+1.

Not exactly what you’re looking for?
Ask My Question
Jeffrey Jordon
Answered 2021-11-03 Author has 2262 answers

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions