How do you simplify sqrt10sqrt8?

2 Answers
Don't Memorise
Jun 15, 2015

= color(red)(4sqrt5

Explanation:

sqrt10sqrt8 = sqrt(80)

sqrt 80 = sqrt(4 . 4 . 5 )

= color(red)(4sqrt5

Bill K.
Jun 17, 2015

If you ever wondered why sqrt(a)sqrt(b)=sqrt(ab) (for a,b \geq 0), the reason follows from the commutative and associative properties of multiplication: (sqrt(a)sqrt(b))^2=(sqrt(a)sqrt(b))*(sqrt(a)sqrt(b))

=(sqrt(a)sqrt(a))*(sqrt(b)sqrt(b))=a*b.

But sqrt(ab) is the unique nonnegative number whose square is ab. Hence sqrt(a)sqrt(b)=sqrt(ab).

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