Question

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

Answer 1

`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`