How do you find the square root of 500?

2 Answers
Mar 2, 2018

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

Mar 2, 2018

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" ")