Question
QUESTION I
1.1 Which of the following numbens is rational?
12 Simplify:
1.1 Which of the following numbens is rational?
12 Simplify:
Ask by Bolton Maxwell. in South Africa
Jan 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Simplified Answers:
-
1.1 Which of the following numbers is rational?
- 2 and 3 are rational numbers.
-
12.1 Simplify:(Alternatively,
.) -
12.2 Simplify:
-
12.3 Simplify:
Solution
Sure, let’s address each part of your questions step by step.
QUESTION I
1.1 Which of the following numbers is rational?
The numbers given are:
Rational numbers are numbers that can be expressed as a fraction
where
and
are integers, and
.
-
: Rational (can be written as ). -
: Rational (can be written as ). -
: This is a complex number ( ), not a rational number. -
: Irrational (it cannot be expressed as a simple fraction). -
: Irrational (17 is not a perfect 8th power).
Answer: 2 and 3 are rational numbers.
12. Simplify the following expressions
12.1 Simplify:
Step-by-Step Solution:
-
Simplify the numerator:
-
Simplify the denominator:
-
Divide the numerator by the denominator:
-
Multiply by 121:
Final Simplified Form:
(This can also be expressed as
if preferred.)
12.2 Simplify:
Step-by-Step Solution:
-
Combine like terms:
-
Take the square root:
Final Simplified Form:
12.3 Simplify:
Step-by-Step Solution:
-
Expand
: -
Expand
: -
Substitute back into the original expression:
-
Distribute the constants:
-
Calculate
: -
Combine like terms:
Final Simplified Form:
If you have any more questions or need further clarification on any of these steps, feel free to ask!
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
Rational numbers are those that can be expressed as the quotient of two integers. In your list,
(as
) and
(as
) are rational. However, both
(since it’s imaginary) and
(which is irrational) do not fit the bill, while
cannot be expressed as a simple fraction either. So, the rational numbers here are
and
!
Now let’s put on our math hats for the simplifications! For
, factor out
from the numerator making it
. This simplifies nicely to
.
For
, combine like terms inside the square root first, giving you
. Then simplify under the radical to get
which results in
. Fun with math!