Describe the possible values of variable a such that (/72) + (/a) can be simplified to a single term.
Note: (/a) is the square root of a.
√72 + √a
= 6√2 + √a
so, if a is of the form 2n^2
6√2 + √2n^2 = (6+√n^2)√2 = (6+n)√2
Ah, discussing math, are we? Well, let's see if I can add some humor to this mathematical equation!
To simplify the expression (/72) + (/a), we need to find a value for variable a that makes the square root term cancel out with the 72 under the other root.
In other words, we need to find a value for a that squashes the square root as if it's being chased by a giant shoe-wearing clown! Squish!
Now, joking aside, let's solve this equation. In order for the square root of a to cancel out with the square root of 72, a must equal 72 squared. Which means a = 72 x 72, which is 5184.
So, if a = 5184, then the expression can be simplified to a single term. I hope I was able to add a dash of humor to your math question!
To simplify the expression (/72) + (/a) to a single term, we need to find values of variable a that result in the two square roots being able to be combined with a common denominator.
The square root of 72 can be simplified as follows:
(/72) = (/2) * (/36) = (/2) * (/6^2) = (/2) * 6 = 6(/2) = 6/2
Now, let's simplify (/a):
(/a) = (/a)
For both expressions to be combined, the denominator of (/a) should be equal to 2. This means that a must be a perfect square with 2 as a factor. Therefore, the possible values of variable a are any perfect squares that are divisible by 2.
For example, a = 4, a = 8, a = 16, a = 36, etc.
In summary, the values of variable a such that (/72) + (/a) can be simplified to a single term are any perfect squares that are divisible by 2 such as a = 4, a = 8, a = 16, a = 36, etc.
To determine the possible values of variable a such that (/72) + (/a) can be simplified to a single term, we need to consider the properties of square roots and the simplification process.
Simplifying the expression (/72) + (/a) involves combining the terms under a common radical. However, this can only be done if the terms have the same radical, or if one term can be simplified to have the same radical as the other.
Let's analyze each term separately:
1. (/72): This term represents the square root of 72. To simplify it, we need to find the prime factors of 72 and group them in pairs, then take the square root.
Prime factors of 72: 2 * 2 * 2 * 3 * 3
Pairing them: (2 * 2) * (2 * 3) * (3)
Taking the square root of each pair: (/4) * (/6) * (3)
Combining the pairs into a single term: (/4 * 6 * 3) = (/72)
So, (/72) is already in its simplified form.
2. (/a): This term represents the square root of a. To determine the values of a that allow the expression to be simplified, we need to find the perfect square factors of a.
For example:
- If a = 36, then (/a) = (/36) = (/6 * 6) = 6
- If a = 16, then (/a) = (/16) = (/4 * 4) = 4
- If a = 25, then (/a) = (/25) = 5
However, if a is not a perfect square, then (/a) cannot be simplified further.
Thus, the possible values of variable a that allow the expression to be simplified to a single term are any values of a that are perfect squares.
In summary, variable a must be a perfect square such as 36, 16, 25, and so on, in order for the expression to be simplified to a single term.