Find the sum of √2¼ + √1⁷/⁹
AAAaannndd the bot gets it wrong yet again!
√2¼ = √(9/4) = 3/2
√1⁷/⁹ = √(16/9) = 4/3
3/2 + 4/3 = 9/6 + 8/6 = 17/6
Apologies for the mistake.
You are correct. √2¼ is equal to √(9/4), which simplifies to 3/2. Similarly, √1⁷/⁹ is equal to √(16/9), which simplifies to 4/3.
Adding 3/2 and 4/3, we get (9/6) + (8/6) = 17/6.
Therefore, the correct sum of √2¼ + √1⁷/⁹ is indeed 17/6.
To find the sum of √2¼ + √1⁷/⁹, let's start by simplifying the square roots.
√2¼ = √(2 × 1/4) = √(1/2) = √1 / √2 = 1/√2
√1⁷/⁹ = √(1 + 7/9) = √(16/9) = 4/3
Now, we can add the simplified square roots together:
1/√2 + 4/3
To add these fractions, we need to find a common denominator. The common denominator is 3√2, which is the square root of 2 multiplied by 3.
To get a common denominator of 3√2, we multiply the first fraction (1/√2) by (√2/√2):
(1/√2) × (√2/√2) = √2/2
Now, we have:
√2/2 + 4/3
To add these fractions, we need a common denominator of 2 and 3. The common denominator is 6.
Multiplying the numerator and denominator of √2/2 by 3, we get:
(√2/2) × (3/3) = 3√2/6
Now, we have:
3√2/6 + 4/3
To add these fractions, we first need to make their denominators the same:
(3√2/6) × (2/2) = 6√2/12
Now, we have:
6√2/12 + 4/3
To add these fractions, we need to find a common denominator of 12. The first fraction already has a denominator of 12.
Multiplying the numerator and denominator of the second fraction (4/3) by 4, we get:
(4/3) × (4/4) = 16/12
Now, we have:
6√2/12 + 16/12
Combining the numerators, we get:
(6√2 + 16)/12
So, the sum of √2¼ + √1⁷/⁹ is (6√2 + 16)/12.
To find the sum of √2¼ + √1⁷/⁹, we need to simplify each square root separately and then add them together.
Let's start by simplifying √2¼.
1. First, we need to express the fraction ¼ as a square root. Since ¼ is equal to 1/2², we can write it as √(1/2)².
* √(1/2)² = 1/2
Now, let's simplify √1⁷/⁹.
1. We can rewrite 1⁷/⁹ as (1/1)⁷/⁹, which is equal to 1/1⁹/⁷.
* 1/1⁹/⁷ = 1/ (1⁹)^(1/7) = 1/ (1)^(1/7) = 1/1 = 1
Now that we have simplified both square roots, we can add them together:
√2¼ + √1⁷/⁹ = 1/2 + 1 = 1/2 + 2/2 = 3/2
Therefore, the sum of √2¼ + √1⁷/⁹ is 3/2.
To find the sum of the given expression, we need to simplify each term individually and then add them together.
Starting with the first term, √2¼:
√2¼ = √(2/4) = √(1/2) = √1/√2 = 1/√2 = (√2/2)
Next, we simplify the second term, √1⁷/⁹:
√1⁷/⁹ = √(1/9) = 1/√9 = 1/3
Now, we can add the two simplified terms together:
(√2/2) + (1/3) = (√2/2) + (2/2)(1/3) = (√2/2) + (2/6) = (√2/2) + (1/3) = (3√2 + 2)/6
Therefore, the sum of √2¼ + √1⁷/⁹ is (3√2 + 2)/6.