How do you simplify sqrt18 div sqrt(8 - 3)?

2 Answers
Don't Memorise
Apr 7, 2015

sqrt18/sqrt(8-3)

= sqrt18/sqrt5

= sqrt(9*2)/sqrt5

= (sqrt9*sqrt2)/sqrt5 We used the Identity sqrt(a*b)=sqrta*sqrtb

= (3*sqrt2)/sqrt5 -------------(a)

Next, we need to RATIONALISE the denominator.
To do that, we multiply the Numerator and the Denominator by sqrt5

= (3*sqrt2)/sqrt5*sqrt5/sqrt5

= (3*sqrt10)/5

The answer can be left in this form, but if you want to find the numerical value of the expression, we can substitute the approximate values of sqrt2 and sqrt5 in (a)

We get ((3) * (1.414))/2.236 ~ 1.9

Meave60
Apr 7, 2015

The answer is 3sqrt(2/5) or (3sqrt10)/5.

sqrt18-:sqrt(8-3) =

sqrt18/sqrt(8-3) =

(sqrt2sqrt9)/(sqrt5) =

(sqrt9=3)

(3sqrt2)/sqrt5 =

3sqrt(2/5)

To remove sqrt5 from the denominator, multiply the numerator and denominator by sqrt5.

(3sqrt2)/(sqrt5)*sqrt5/sqrt5 =

(3sqrt2*sqrt5)/5 =

(3sqrt10)/5

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