Question

Find √10 to the nearest hundredth.Explain how you found your answer.

Answer 1

the square root of 10 is 3.16 because 3.16 times 3.16 equals 10

Answer 2

Answer: 3.16

Step-by-step explanation:

We do know (without calculator) the square root of 9 and of 16

$\sqrt{9} = 3$

$\sqrt{16} = 4$

And we know that $9 < 10 < 16$

So, $\sqrt{9} <\sqrt{10} <\sqrt{16}$

$3 < \sqrt{10} < 4$

So $\sqrt{10}$ is in the middle of 3 and 4, and because 10 is closer to 9 than to 16, the $\sqrt{10}$ is closer to 3.

Now,

We divide $\frac{10}{3} = 3.33$

And we average 3 and 3.33: $\frac{3+3.33}{2} = 3.17$

Again, $\frac{10}{3.17} = 3.16$  

And if we make with calculator $\sqrt{10} = 3.162278$

So the value that we find is good $\sqrt{10} = 3.16$