How do you simplify #sqrt70 ÷ sqrt10#?

1 Answer
Aug 11, 2015

Answer:

#sqrt(7)#

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# as

#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))#