Add 3 21−−√ + 7 21−−√ .
Add 19−−√ + 19
Add 22−−√3 + 322−−√ + 22−−√
Subtract 8 23−−√−23−−√.
jake runs 76–√ miles on Monday and 56–√ miles on Tuesday. What is the difference in miles run each day?
To add 3\u221221−√ + 7\u221221−√, we can combine the terms with the same radical. This gives us (3 + 7) √21 = 10 √21.
To add 19−√ + 19, we simply add the numbers outside the radical. This gives us 2√19.
To add 22−√3 + 32−√ + 22−√, we can also combine the terms with the same radical. This gives us (22 + 3 + 2) √3 = 27 √3.
To subtract 8\u221223−√−23−√, we can simply subtract the numbers outside the radical. This gives us -15√3.
The difference in miles run each day is found by subtracting the distance run on Tuesday from the distance run on Monday.
So, the difference is 76 – 56 = 20 miles.
To add 3√21 + 7√21, you can combine the terms with the same radical:
3√21 + 7√21 = (3 + 7)√21 = 10√21
To add √19 + √19, you can also combine the terms with the same radical:
√19 + √19 = (1 + 1)√19 = 2√19
To add √3 + 32√2 + √2, you can combine the terms with the same radical:
√3 + 32√2 + √2 = √3 + (32 + 1)√2 = √3 + 33√2
To subtract 8√23 - √23, you can combine the terms with the same radical:
8√23 - √23 = (8 - 1)√23 = 7√23
The difference in miles run each day between 76√ and 56√ can be found by subtracting the two distances:
76√ - 56√ = (76 - 56)√ = 20√ miles
To add or subtract square roots, we need to have the same terms inside the square roots.
1. Add 3√21 + 7√21:
Since both terms have the same square root (√21), we can simply add the coefficients (numbers in front of the square root):
3√21 + 7√21 = (3 + 7)√21 = 10√21.
2. Add √19 + 19:
Here, we don't have a similar term to combine with √19, so we keep it separate:
√19 + 19.
3. Add √3 + 32√2 + √2:
Again, we can combine the coefficients of the square roots that are the same:
√3 + 32√2 + √2 = √3 + (32 + 1)√2 = √3 + 33√2.
4. Subtract 8√23 - √23:
To subtract, we treat it just like addition, but change the sign (subtract instead of adding):
8√23 - √23 = (8 - 1)√23 = 7√23.
5. Difference in miles run each day:
To find the difference, subtract the number of miles run on Tuesday from the number of miles run on Monday:
76√ - 56√ = 20√.