How can I solve this problem, I'm stuck on it:
Approximate to the nearest hundreth by interpolation
5*square root of 84.4
Thanks
-MC
You probably need to use some tables to interpolate.
But without those, nine squared is 81
10 squared is 100
Using that, which is rather loose, then
the difference in 84.4 and 81 is 3.4
the difference in 81 and 100 is 19
so 3.4/19 = x/1 where x is the addition to 9.0
x=.179
Square root of 84.4 then is 9.18 to the nearest hundredth, approximately
Thank you so much bobpursley!
-MC
To approximate to the nearest hundredth by interpolation, you can use the concept of linear interpolation. Here's how you can solve the problem step by step:
Step 1: Find the two nearest perfect squares to 84.4. The perfect squares closest to 84.4 are 81 (9^2) and 100 (10^2).
Step 2: Calculate the difference between the given number (84.4) and the smaller square (81). In this case, the difference is 84.4 - 81 = 3.4.
Step 3: Calculate the difference between the larger square (100) and the smaller square (81). In this case, the difference is 100 - 81 = 19.
Step 4: Divide the difference between the given number and the smaller square (step 2) by the difference between the larger square and the smaller square (step 3). In this case, 3.4 / 19 = 0.1789.
Step 5: Multiply the result from step 4 by the difference between the two nearest whole numbers. In this case, multiply 0.1789 by 10 (since 10 - 9 = 1). The result is 0.1789 * 10 = 1.789.
Step 6: Add the result from step 5 to the smaller whole number. In this case, add 1.789 to 9 (the smaller whole number). The result is 10.789.
Step 7: Round the result to the nearest hundredth. In this case, rounding 10.789 to the nearest hundredth gives 10.79.
Therefore, the approximate value of 5 times the square root of 84.4, rounded to the nearest hundredth, is 10.79.