The irrational numbers are numbers that cannot be expressed as a fraction (ratio) of two integers.
To determine which expressions will result in an irrational number, we need to check if any of the expressions involve square roots.
1. M + N = √2 + √5 - This expression involves the sum of two square roots, so it may result in an irrational number.
2. M * N = √2 * √5 = √10 - This expression also involves the product of two square roots, so it may result in an irrational number.
3. S + T = 2 + 5 = 7 - This expression involves the sum of two integers, so it results in a rational number.
4. S * T = 2 * 5 = 10 - This expression involves the product of two integers, so it results in a rational number.
5. M * S = √2 * 2 = 2√2 - This expression involves the product of an integer and a square root, so it may result in an irrational number.
6. N + T = √5 + 5 - This expression involves the sum of a square root and an integer, so it may result in an irrational number.
7. N^2 = (√5)^2 = 5 - This expression involves squaring a square root, so it results in a rational number.
Therefore, the expressions that may result in an irrational number are 1, 2, 5, and 6: M + N, M * N, M * S, and N + T.
So the correct answers are:
1. M + N
2. M * N
5. M * S
6. N + T
Given:
M = √2
N = √5
S = 2
T = 5
Which expression will result in an irrational number? Select all that apply.
1. M + N
2. M * N
3. S + T
4. S * T
5. M * S
6. N + T
7. N^2
1 answer