Question

How do you find the square root of 500?

Answer 1

the answer is `10sqrt(5)`

Explanation:

`100 *5` gives you `500` now `10*10` gives you `100` now you have two `10s` and you get `5,2` for both `10s` and you have a pair of `5` and a pair of `2` put the `5` earlier doesn't have a partner so you keep him inside b/c he doesn't have anyone

Answer 2

We get `22.360` up to three decimal places.

Explanation:

As the given number is not a perfect square, the square root of this number will be a decimal number.
We must, therefore, state the accuracy to which the square root is to be calculated.

Suppose we need to calculate the `sqrt500` to an accuracy of three decimal places.

Step 1. Make pairs of digits starting from Units place.
we get `5bar00`.

Step 2. Consider the unpaired digit and calculate the nearest digit which is just lower than the square root of this digit. We consider `5.` The nearest digit is `2` as `3^2=6>5`.

We get first digit of the answer. Workout the remainder which `=1`. Bring down the next pair which is `bar00`. Makes the dividend `=100`. Also add the answer digit to the divisor. We have `2+2=4`

Step 3. Place highest digit in units place of divisor to make the divisor which will divide dividend `100`. We see that it can be divided with `2xx42`. `:.3xx43>100`.
Complete the division. Nearest digit is `2`. Complete the division and obtain remainder. `=100-84=16`. Also add the answer digit so obtained to divisor. We get `42+2=44` for the next step.

Step 4. Next we have decimal in the original number. Place it after the quotient `22` and bring a pair of zeros down. The dividend becomes `1600`

Continue steps till three places of decimal.

We see that in the Step 5. Number remaining is `304.` Adding two zeros makes it `30400` We are not able to divide the dividend because even with digit `1` placed at units place of divisor the product of quotient digit and divisor is `>` the dividend. We place a `0` in the quotient place and add two zeros to the dividend

`2|bar(5bar00.bar(00)\ bar(00)\ bar00\ bar00(22.360`
`ul(2|4)\darr`
`42|100`
`ul(\ 2|" "84)darr`
`443|1600`
`ul(" "3|1329)darr`
`4466|27100`
`ul(" "6|26796)darrdarr`
`44820|3040000`
`ul(" "0" ")`