How do you simplify $(7sqrt100)/sqrt500$ ?

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Answer 1 · 2015-10-01T00:17:42

The answer is $(7sqrt5)/5$ .

$(7sqrt100)/(sqrt500)$

Numerator
Write the prime factorization for $100$ and simplify. Use the square root rule $sqrt(a^2)=absa$ .

$7sqrt100=7sqrt(10xx10)=7sqrt(10^2)=7xx10=70=$

$70/(sqrt500)$

Denominator
Write the prime factorization for $sqrt500$ and simplify. Again use the square root rule $sqrt(a^2)=absa$ .

$sqrt500=sqrt(2xx2xx5xx5xx5)=sqrt(2^2xx5^2xx5)=2xx5sqrt5=10sqrt5$

Recombine the numerator and denominator.

$70/(10sqrt5)$

Rationalize the denominator.

$(7)/(sqrt(5)) * (sqrt5)/(sqrt5)=$

$(7sqrt5)/(sqrt(25))$

Write the prime factors for $25$ .

$sqrt25=sqrt(5xx5)=$

$sqrt25=sqrt(5^2)$

Apply the square root rule $sqrt(a^2)=absa$ and simplify.

$(7sqrt5)/5$

How do you simplify (7sqrt100)/sqrt500(7sqrt100)/sqrt500?