simplify 13 square root (27)
To simplify this expression, we can start by finding the square root of 27. The square root of 27 is 3√3.
Therefore, 13√27 simplifies to 13 * 3√3, which can be further simplified as 39√3.
To simplify the expression 13√27, we can first break down √27 into its simplest form.
Step 1: Find the prime factors of 27.
The prime factorization of 27 can be obtained by dividing it by prime numbers until we can no longer do so. 27 can be divided by 3, resulting in 9 and then 3 again, resulting in 3. So, the prime factorization of 27 is 3 x 3 x 3.
Step 2: Simplify the square root.
Since there are two 3's inside the square root, we can remove one of them and write it as √(9 x 3). We can then simplify this expression further to √9 x √3.
Step 3: Simplify the square root of 9.
The square root of 9 is 3, so we have 3 x √3.
Step 4: Multiply the coefficient outside the square root.
The coefficient outside the square root is 13. Multiply it by the simplified square root expression of 3 x √3 to get the final result.
Final Answer:
13 x 3 x √3 = 39√3
To simplify the expression 13√27, we can break down the radicand, which is 27, into its prime factors.
First, we divide 27 by the smallest prime number, which is 3.
27 ÷ 3 = 9
Next, we repeat the process with the quotient 9.
9 ÷ 3 = 3
Since 3 is also a prime number, we can't divide it further. Therefore, the prime factorization of 27 is 3 × 3 × 3, or 3^3.
Now, we can rewrite the expression as:
13√(3^3)
Using the property of radicals, we can move the exponent outside the radical:
13 × √3 × √3 × √3
Simplifying further, we have:
13 × 3 × √3
And finally, multiplying the coefficients, we get:
39√3
Therefore, the simplified expression of 13√27 is 39√3.