Simplify 13√27
To simplify the expression 13√27, we can simplify the square root of 27 first.
The prime factorization of 27 is 3 * 3 * 3.
We can pair the prime factors in sets of two because each pair will simplify to a single factor outside the square root sign. However, there is one remaining factor of 3 that cannot be simplified.
So, 27 can be written as 3 * 3 * √3.
Now, we can simplify the expression 13 * √27 by multiplying the values outside and inside the square root.
13 * √27 = 13 * (3 * 3 * √3) = 39 * √3.
Therefore, the simplified form of 13√27 is 39√3.
To simplify 13√27, we need to find the largest perfect square that can be factored out from 27.
The largest perfect square that divides 27 is 9 (3^2), since 9 is the largest perfect square less than 27.
So, we can rewrite 27 as 9 * 3:
13√27 = 13√(9 * 3)
Next, we can use the property of square roots to split the square root:
= 13(√9 * √3)
The square root of 9 is 3:
= 13(3 * √3)
= 39√3
Therefore, 13√27 simplifies to 39√3.
how?
To simplify √27, we need to find the largest perfect square that can be divided into 27. In this case, the largest perfect square is 9, which is the square of 3. Therefore, we can rewrite 27 as 9 * 3.
So, 13√27 can be simplified as 13√(9 * 3).
Using the product rule of square roots, we can break down the expression further: 13√(9 * 3) = 13√9 * √3.
Since √9 equals 3, we can simplify the expression as: 13 * 3√3.
Therefore, 13√27 simplifies to 39√3.
I apologize for the incorrect response earlier.
To simplify 13√27, we can simplify the square root of 27.
The prime factorization of 27 is 3 * 3 * 3.
Since the square root of 9 (3 * 3) is 3, we can take out a factor of 3 from the square root:
√27 = √(9 * 3) = √(9) * √(3) = 3 * √3
Therefore,
13√27 = 13(3 * √3) = 39√3