Question

How do you simplify `sqrt(5.6)`?

Answer 1

`(2sqrt35)/5=2/5sqrt35`

Explanation:

`"using the "color(blue)"laes of radicals"`

`•color(white)(x)sqrtaxxsqrtb=sqrt(ab)" and "sqrtaxxsqrta=a`

`•color(white)(x)sqrt(a/b)=sqrta/sqrtb`

`"note that "5.6=56/10`

`rArrsqrt5.6=sqrt(56/10)=sqrt56/sqrt10`

`"and "sqrt56=sqrt(4xx14)=sqrt4xxsqrt14=2sqrt14`

`rArrsqrt56/sqrt10=(2sqrt14)/sqrt10`

`color(blue)"rationalise the denominator"`

`"multiply numerator/denominator by "sqrt10`

`rArr(2sqrt14)/sqrt10xxsqrt10/sqrt10`

`=(2sqrt140)/10=(2xx2sqrt35)/10=(4sqrt35)/10=2/5sqrt35`