How do you simplify this? " "sqrt(3) + sqrt(1/3) 3+13

3 Answers
May 21, 2018

sqrt3+sqrt(1/3)=4/sqrt33+13=43

Explanation:

sqrt3+sqrt(1/3)3+13

sqrt3=3/sqrt3=3=33=

sqrt(1/3)=1/sqrt313=13

sqrt3+sqrt(1/3)=3/sqrt3+1/sqrt33+13=33+13
=(3+1)/sqrt3=4/sqrt3=3+13=43
Thus,

sqrt3+sqrt(1/3)=4/sqrt33+13=43

May 21, 2018

=4/3 sqrt3=433

Explanation:

You can write the square root of the fraction as separate roots:

sqrt3 + color(blue)(sqrt(1/3)) = sqrt3 + color(blue)(sqrt1/sqrt3)3+13=3+13

sqrt3 + 1/sqrt3" "larr3+13 rationalise the denominator

=sqrt3 +1/sqrt3 xx sqrt3/sqrt3=3+13×33

=sqrt3 +sqrt3/3" "larr=3+33 factor out sqrt33

=sqrt3(1+1/3)=3(1+13)

=4/3 sqrt3=433

May 21, 2018

sqrt3+ sqrt(1/3)3+13 is not an equation and, therefore, cannot be solved but it can be rationalized.

Explanation:

sqrt3+ sqrt(1/3)3+13

Separate the second term into a radical over a radical:

sqrt3+ sqrt1/sqrt33+13

Multiply the second term by 1 in the form of sqrt3/sqrt333

sqrt3+ sqrt1/sqrt3sqrt3/sqrt33+1333

Because of sqrt3sqrt3=333=3: the denominator becomes 3:

sqrt3+ sqrt3/33+33

Multiply the first term by 1 in the form of 3/333:

(3sqrt3)/3+ sqrt3/3333+33

The two fractions can be combined over the common denominator:

(3sqrt3+ sqrt3)/333+33

Add the terms in the numerator

(4sqrt3)/3433

The above is the rationalized and simplified form.