Question

How do you find a one-decimal place approximation for `-sqrt20`?

Answer 1

-4.4

Explanation:

You would look at the radical. You know that 20 is not a perfect square. But what are the perfect squares that are close to it? 16 is the closest perfect square less than 20; its square root is 4. The closest perfect square greater than 20 is 25; its square root is 5.

Which perfect square is 20 closer to? It's 16, so the tenths place would be a little closer to the square root of 16 (4). Since we know the square root is greater than 4 and less than 5, we know that it would be around 4.4, since it's somewhere in the middle between 4 and 5 but a little closer to the lesser side (the 4).

You would then take the opposite of it since the negative sign is outside the radical.