Question

How do you simplify `sqrt1500/sqrt9.8?`

Answer 1

`color(crimson)(=> sqrt(7500 / 49)color(blue)(= 12.3718`

Explanation:

`sqrt1500 / sqrt 9.8`

`=> sqrt(1500/9.8)`

`=> sqrt ((1500*5) / (9.8 * 5))`

`color(crimson)(=> sqrt(7500 / 49)`

`color(blue)(=> 12.3718`

Answer 2

`(50sqrt3)/7`

Explanation:

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

`•color(white)(x)sqrta/sqrtbhArrsqrt(a/b)`

`•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)`

`sqrt1500/sqrt9.8`

`=sqrt(1500/9.8)`

`=sqrt(1500xx10)/(9.8xx10)`

`=sqrt(15000/98)`

`=(100sqrt1.5)/(7sqrt2)`

`=(100sqrt(3/2))/(7sqrt2)`

`=(100sqrt3)/(7sqrt2xxsqrt2)=(100sqrt3)/14=(50sqrt3)/7`