How do you simplify #sqrt70 ÷ sqrt10#?
1 Answer
Explanation:
You can actually simplify this expression by using the product property and the quotient property of radicals.
- using the product property
The product property tells you that you have
#color(blue)(sqrt(a * b) = sqrt(a) * sqrt(b))#
In your case, you can write
#sqrt(70) = sqrt(7 * 10) = sqrt(7) * sqrt(10)#
This means that the expression can be simplified to
#sqrt(70)/sqrt(10) = (color(red)(cancel(color(black)(sqrt(10)))) * sqrt(7))/color(red)(cancel(color(black)(sqrt(10)))) = color(green)(sqrt(7))#
- using the quotient property
The quotient property tells you that you have
#color(blue)(sqrt(a/b) = sqrt(a)/sqrt(b))# , where#sqrt(b)!=0#
In your case, you can write
#sqrt(70)/sqrt(10) = sqrt(70/10) = sqrt((7 * color(red)(cancel(color(black)(10))))/color(red)(cancel(color(black)(10)))) = color(green)(sqrt(7))#
