How do you simplify $sqrt70 ÷ sqrt10$ ?

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Answer 1 · 2015-08-11T12:53:35

$sqrt(7)$

You can actually simplify this expression by using the product property and the quotient property of radicals.

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

$sqrt(70)/sqrt(10) = (color(red)(cancel(color(black)(sqrt(10)))) * sqrt(7))/color(red)(cancel(color(black)(sqrt(10)))) = color(green)(sqrt(7))$

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

$sqrt(70)/sqrt(10) = sqrt(70/10) = sqrt((7 * color(red)(cancel(color(black)(10))))/color(red)(cancel(color(black)(10)))) = color(green)(sqrt(7))$

How do you simplify sqrt70 ÷ sqrt10sqrt70 ÷ sqrt10?