How do you find the square root of 500?

2 Answers
Mar 2, 2018

Answer:

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

Answer:

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" ")#