How do you simplify (18+sqrt567)/918+√5679?

1 Answer
CountryGirl
Jun 11, 2018

2 + sqrt72+√7

Explanation:

Begin by simplifying the radical, and making any squares possible inside the radical.

(18 + sqrt567)/918+√5679 rArr (18 + sqrt(3^2 * 3^2 * 7))/9⇒18+√32⋅32⋅79

Now take the squares out and multiply their roots outside the radical:

(18 + sqrt(3^2 * 3^2 * 7))/9 rArr18+√32⋅32⋅79⇒ (18 + (3 * 3)sqrt7)/918+(3⋅3)√79 rArr (18 + 9sqrt7)/9⇒18+9√79

Now simplify the top and bottom of the expression by canceling out 99:

(stackrel2cancel18 + stackrel1cancel9sqrt7)/cancel9_1 rArr (2 + 1sqrt7)/1 rArr 2 + sqrt7

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