To determine which of the following are examples of rational numbers, we need to check if the numbers can be expressed as a fraction in the form of p/q, where p and q are integers and q is not equal to 0.
Let's solve each option step by step:
Option 1: √4 + √16
√4 = 2
√16 = 4
2 + 4 = 6
This number, 6, can be expressed as 6/1, which is a ratio of two integers. Therefore, √4 + √16 is a rational number.
Option 2: √5 + √36
√5 is an irrational number because we cannot find a perfect square root of 5.
√36 = 6
Since one term is irrational, the sum is also irrational. Therefore, √5 + √36 is not a rational number.
Option 3: √9 + √24
√9 = 3
√24 is an irrational number since it cannot be expressed as a perfect square root.
Since one term is irrational, the sum is also irrational. Therefore, √9 + √24 is not a rational number.
Option 4: 2√4
2√4 = 2 * 2 = 4
This number, 4, can be expressed as 4/1, which is a ratio of two integers. Therefore, 2√4 is a rational number.
Option 5: √49 * √81
√49 = 7
√81 = 9
7 * 9 = 63
This number, 63, can be expressed as 63/1, which is a ratio of two integers. Therefore, √49 * √81 is a rational number.
Option 6: 3√12
√12 is an irrational number since it cannot be expressed as a perfect square root.
Since one term is irrational, the product is also irrational. Therefore, 3√12 is not a rational number.
In conclusion, the rational numbers among the given options are:
√4 + √16
2√4
√49 * √81
Which of the following are examples of rational numbers? Select all that apply.
√4+ √16
√5+√36
√9+ √24
2*√4
√49 * √81
3√12
Solve step by step
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1 answer