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

3 Answers
Shiva Prakash M V
May 21, 2018

sqrt3+sqrt(1/3)=4/sqrt3√3+√13=4√3

Explanation:

sqrt3+sqrt(1/3)√3+√13

sqrt3=3/sqrt3=√3=3√3=

sqrt(1/3)=1/sqrt3√13=1√3

sqrt3+sqrt(1/3)=3/sqrt3+1/sqrt3√3+√13=3√3+1√3
=(3+1)/sqrt3=4/sqrt3=3+1√3=4√3
Thus,

sqrt3+sqrt(1/3)=4/sqrt3√3+√13=4√3

EZ as pi
May 21, 2018

=4/3 sqrt3=43√3

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+√1√3

sqrt3 + 1/sqrt3" "larr√3+1√3 ← rationalise the denominator

=sqrt3 +1/sqrt3 xx sqrt3/sqrt3=√3+1√3×√3√3

=sqrt3 +sqrt3/3" "larr=√3+√33 ← factor out sqrt3√3

=sqrt3(1+1/3)=√3(1+13)

=4/3 sqrt3=43√3

Douglas K.
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/sqrt3√3+√1√3

Multiply the second term by 1 in the form of sqrt3/sqrt3√3√3

sqrt3+ sqrt1/sqrt3sqrt3/sqrt3√3+√1√3√3√3

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

sqrt3+ sqrt3/3√3+√33

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

(3sqrt3)/3+ sqrt3/33√33+√33

The two fractions can be combined over the common denominator:

(3sqrt3+ sqrt3)/33√3+√33

Add the terms in the numerator

(4sqrt3)/34√33

The above is the rationalized and simplified form.

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