How do you simplify #3sqrt32-4sqrt63#?

1 Answer
May 31, 2016

Answer:

#12sqrt2-12sqrt7#

Explanation:

To simplify a radical means to express it in the form #asqrtb#

where a is a rational number and #sqrtb,# is a surd.

Rational numbers can be expressed in the form #a/b# where a and b are integers.

example : #1/2,2/3,7/8" and " 4" as 4"=4/1#

numbers which cannot be expressed in this form are called irrational. #pi# being an example of one.

A surd is a radical which cannot be reduced to a whole number.

#sqrt9=3" is not a surd but "sqrt3" is not a whole number and so is a surd."#

now #sqrt32=sqrt(16xx2)=sqrt16xxsqrt2=4sqrt2#

and #sqrt63=sqrt(9xx7)=sqrt9xxsqrt7=3sqrt7#

#rArr3sqrt32-4sqrt63=3xx4sqrt2-4xx3sqrt7#

#=12sqrt2-12sqrt7#