# How do you simplify sqrt(7+sqrt4)?

Jul 23, 2015

You take the square root of $4$ first, then take the square root of the resulting expression.

#### Explanation:

Notice that your expression contains the square root of $4$, which a perfect square. More specifically,

4 = 2 * 2 = 2""^2

This means that you can write

sqrt(7 + sqrt(4)) = sqrt(7 + sqrt(2""^2)) = sqrt(7 + 2) = sqrt(9)

This time you come across the square root of $9$, which is another perfect square.

9 = 3 * 3 = 3""^2

sqrt(9) = sqrt(3""^2) = 3
$\sqrt{7 + \sqrt{4}} = \sqrt{7 + 2} = \textcolor{g r e e n}{3}$