-Determine the two consecutive integers the radical lies between.
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# -Determine the two consecutive integers the radical lies between.

[From: ] [author: ] [Date: 12-06-11] [Hit: ]
a negative outside of the square root of 30. (30 is positive.) 2. cubic root of 50.3. negative outside of the square root of 10.......
-Can you leave a little explanation on how to solve them.
thank, you.
Aileen G.

1. a negative outside of the square root of 30. (30 is positive.)
2. cubic root of 50.
3. negative outside of the square root of 10. (10 is positive.)

1. Square root of 8100
2. cubic root of 0.027
3. square root of 0.01
4. square root of 0.0064

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To determine the two consecutive integers you will want to reference some perfect squares that you know.

1) -√30 is between -√36 and -√25 and therefore is between -6 and -5 since √36=6 and √25=5
2) we know that 4^3= 64 and 3^3=27 so the cubic root of 64 is 4 and the cubic root of 27 is 3. Therefore the cubic root of 50 is between 3 and 4.
3) -√10 is between -√9 and -√16. Once again since √9=3 and √16=4 we know that -√10 must be between -3 and -4

To simplify radicals you need to find factors of the number that are perfect squares to simplify square roots and perfect cubes to simplify cubic roots.

For the square root of 8100 we know that its factors are 81*100, both of which are perfect squares so we have √(8100)= √(81*100) = √81*√100 (by properties of radicals) = 9*100 =900

Or if you had recognized that 8100 is a perfect square right away you could skip right to 900.

2. 0.027 = 27/1000. 27 is a perfect cube and so is 1000 since 3^3=27 and 10^3=1000 so once again using our properties of radicals we can say cube root of 0.027= cube root of (27/1000) = 3/10 = 0.3

Once again you may have been able to recognize it right off as a perfect cube but it may not be too obvious. You can always factor and I find fractions easier to factor than decimals, but that could just be me.

3. square root of 0.01 = √(1/100). 100 is 10^2 and thus a perfect square so its square root is 10. Also the square root of the top, 1, is just 1 since 1^2=1
Thus we have 0.01 = √(1/100) = 1/10 = 0.1

4. 0.0064= 64/10000 Now we will note that the top is a perfect square, 8^=64 and so is the bottom 100^2=10000 so taking the square root of the whole thing is square root of the top over square root of the bottom by our radical rules which gives:
√0.0064 = √(64/10000) = √64/√10000 = 8/100 = 0.08

Hope that helps!
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