# What's the square root of 100000?

Nov 1, 2016

$\sqrt{10} = 3.16227766$

$\sqrt{\text{10 00 00}} = 316.227766 \approx 316.23$

#### Explanation:

Obviously one could plug this into a calculator and get the answer. But what answer can we expect?

Underneath the square root sign - pair the digits from the right.

$\sqrt{\text{10 00 00}}$

Each pair of 0's represents a place in the answer.

The answer will have 3 digits before the comma.
Find them by finding $\sqrt{10}$ on a calculator.

$\sqrt{10} = 3.16227766$

$\sqrt{\text{10 00 00}} = 316.227766 \approx 316.23$

compare the following answers:

$\sqrt{10} = 3.1623 \text{ } \sqrt{100} = 10$

$\sqrt{1000} = 31.623 \text{ } \sqrt{10000} = 100$

$\sqrt{100000} = 316.23 \text{ } \sqrt{1000000} = 1000$

$\sqrt{10000000} = 3162.3 \text{ } \sqrt{100000000} = 10000$

(odd number of 0's)$\text{ }$(even number of 0s)