Roots of Irrational Numbers???

Question

A. Between what two consecutive integers do each of the following numbers like?

1. square root of 21
2. square root of 50
3. square root of 70
4. square root of 98
5. square root of 145
6. square root of 250
7. square root of 310
8. square root of 450
9. square root of 555
10. square root of 650
11. cube root of 16
12. cube root of 60
13. cube root of 200
14. fifth root of 150
15. fourth root of 175



B. Find a one-decimal place approximation for each of the following expressions:

1. square root of 10
2. square root of 18
3. square root of 30
4. square root of 37
5. square root of 50
6. cube root of 8
7. fifth root of 26
8. fourth root of 45
9. square root of 65
10. cube root of 99
11. negative square root of 20
12. negative cube of 35
13. negative fourth root of 200
14. cube root of 15
15. cube root of 30




Pls. help me pls. i need it now pls. pls. i'm begging you pls. pls. pls. very pls.

Answer 1

Most calculators have a button that looks like " x ^ y " that allows you to take any root. Such as the calculator that comes with Microsoft Windows, if that's the OS you're using (change the view from "Standard" to "Scientific" to see that button). For example,

(15) 4th root of 175 is calculated as 175 ^ 1/4 = 3.6, so your answer is "between 3 and 4." Check: 3^4 = 81 and 4^4 is 256; 175 lies between them.

All of the first set can be solved this way.

I'm not sure what your instructor wants for the second batch, since all you have to do is run them through the calculator and write down the answer to one decimal place.

Answer 2

To find the numbers on either side of a root, try various integers:

The numbers you are asked to find are low enough that you could set a table:

5 column, 20 rows.

in the top row, title each column:

power 1, power 2, power 3, power 4, power 5

in the first column (power 1), write the numbers:

2 to 10, then every 2 (12, 14, 16, 18, 20 ... up to 30)

In 2nd column (power 2) take the number of column 1 (power 1) and multiply it by itself.

2 times 2 is 4, write 4
3 times 3 is nine...
and so on.

For the thrid column, multiply the second number by the first.
4 times 2 is 8.
8 goes in the third column (power 3), in the row that begins with number 2 (8 is the cube of 2)

9 times 3 is 27
and so on.

For the 4th column, take third column, multiply by power 1

8 times 2 is 16 (the 4th power of 2)
27 times 3 is 81 (the 4th power of 3)
and so on.

Finally, for fifth column
16 times 2 is 32 (the 5th power of 2)
81 times 3 = 243

Then, when you are asked for the square root of a number, look for that number in the "power 2" column. Very likely, you will find a number higher than it and a number lower than it. You read the roots of these numbers in column "power 1"


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Doing the table will help you remember a few key powers, helping you (in the future) to make very good guesses at various roots.

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The table will help you with B.

For example; square root of 10.

the square of 3 is 9 and the square of 4 is 16
so you know that the answer will be between 3 and 4 (and closer to 3 than 4).

You could try 3.1 (3.1 times 3.1 = 9.61)
then 3.2 times 3.2 = 10.24

3.2 gives a square that is closer to 10 than 3.1 was, so I'd pick 3.2 as the one-decimal approximation.