Question #1 - I dont understand the last step which is = (3a +1) √a
√9a^3 + √a
= √9 √a² · a + √a
= 3√a² · √a + √a
= 3a√a + √a
= (3a +1) √a
Question #2 - again I dont understand how from√9² x² + 9² to √9² (x² +1)
√81x² +81
= √9² x² + 9²
= √9² (x² +1)
= 9√x² + 1
Thanks :)
= 3a√a + √a
= √a(3a + 1) , √a is a common factor
√9² x² + 9²
= 9x^2 + 81
= 9(x^2 + 9)
the step from = √9² x² + 9²
to √9² (x² +1) is incorrect
Question #1: To understand the last step, let's go through the steps one by one.
Starting with √9a^3 + √a:
Step 1: We can simplify the square root of 9a^3 as √9 * √a^2 * √a.
Step 2: √9 is simply 3, and √a^2 is just a. So, we get 3a√a * √a + √a.
Step 3: Multiplying 3a√a * √a gives us 3a√(a * a) = 3a√(a^2) = 3a * a = 3a^2.
Step 4: So, we now have 3a^2 + √a.
Step 5: Notice that we have a common factor of √a. We can factor it out, so our expression becomes (√a) * (3a + 1).
Therefore, the final step is (3a + 1)√a.
Question #2: Similar to the previous question, let's break down the steps:
Starting with √81x² + 81:
Step 1: We can simplify the square root of 81x² as √(9^2 * x^2).
Step 2: Using the property of square roots, we can rewrite the expression as √9² * (x² + 1).
Step 3: √9 is 3, so we get 3 * (x² + 1).
Therefore, the final step is 3(x² + 1).
I hope this explanation helps you understand the steps involved! Let me know if you have any further questions.