How do you simplify sqrt28/sqrt7?

2 Answers
Nam D.
Mar 18, 2018

2

Explanation:

Given: sqrt(28)/sqrt(7)

We got:

sqrt(28)=sqrt(4*7)

=sqrt(4)*sqrt(7)

=2*sqrt(7)

2sqrt(7)

So, the expression becomes:

(2sqrt(7))/sqrt(7)

=(2color(red)cancelcolor(black)(sqrt(7)))/color(red)cancelcolor(black)(sqrt(7))

=2

Meave60
Mar 18, 2018

(sqrt28)/(sqrt7)=color(blue)2

Explanation:

Simplify:

(sqrt28)/(sqrt7)

Rationalize the denominator by multiplying the numerator and denominator by sqrt7.

(sqrt28sqrt7)/(sqrt7sqrt7)

Apply rule: sqrtasqrta=a

(sqrt28sqrt7)/7

Prime factorize sqrt28.

(sqrt(2^2*7)sqrt7)/7

Apply rule: sqrt(a^2)=a

(2sqrt7sqrt7)/7

Apply rule: sqrtasqrta=a

(2xx7)/7

Cancel 7.

(2xxcolor(red)cancel(color(black)(7))^1)/color(red)cancel(color(black)(7))^1

Simplify.

2

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