What square number divides exactly into 50? Is it 25? Which of the surds below can be simplified to have the same base as `4sqrt(3)`  ?  a) `sqrt(8)` b) `sqrt(12)`

Expert Answers
lemjay eNotes educator| Certified Educator

(I) To solve, apply the divisibility rules of numbers. Since 50 ends with 0, it means that it is divisible by the prime numbers 2 and 5.

`50 -:2 = 25`

`50-:5=10`

Between these two results, 25 is a perfect square number.

Therefore, a square number that divides exactly into 50 is 25.

(II) To simplify the radical numbers, factor each number. Then, take the square root of each factor.

(a) `sqrt8 = sqrt(4*2) = sqrt4*sqrt2=2sqrt2`

(b) `sqrt12=sqrt(4*3)=sqrt4*sqrt3=2sqrt3`

Therefore, between these two surds, it is `sqrt12` that simplifies to `2sqrt3` .