Which statements are true? Select the two correct answers. The square root of a positive number greater than 1 is less than the number.
The square root of a positive number is always less than half of the number itself.
The square root of a positive number less than 1 is less than the number.
The square root of a perfect square is not a whole number.
The square root of a positive number less than 1 is between 0 and 1.

Step-by-step explanation:

The square root of a positive number is greater than the number when it is less than 1, and less than the number when it is greater than 1. Consider, for example, ...

  √9 = 3 . . . . 3 is less than 9, and a whole number

  √0.09 = 0.3 . . . . 0.3 is greater than 0.09 (and more than 0.09/2)

So, the correct statements about square roots are ...

The square root of a positive number greater than 1 is less than the number.

The square root of a positive number less than 1 is between 0 and 1.

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step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for