Certainly! Let's simplify the expression [tex]\( 6 \sqrt{11} + 5 \sqrt{11} \)[/tex] step-by-step:
1. Identify like terms: Both terms [tex]\( 6 \sqrt{11} \)[/tex] and [tex]\( 5 \sqrt{11} \)[/tex] contain the square root of 11, making them like terms.
2. Combine like terms: Since they are like terms, we can add the coefficients (the numbers in front of the square roots). Therefore:
[tex]\[
(6 + 5) \sqrt{11}
\][/tex]
3. Perform the addition of the coefficients: Add the numbers 6 and 5:
[tex]\[
6 + 5 = 11
\][/tex]
4. Rewrite the expression with the combined coefficient:
[tex]\[
11 \sqrt{11}
\][/tex]
Therefore, the simplified form of [tex]\( 6 \sqrt{11} + 5 \sqrt{11} \)[/tex] is [tex]\( 11 \sqrt{11} \)[/tex].
To express it numerically:
5. Calculate the numerical value of [tex]\( 11 \sqrt{11} \)[/tex]:
[tex]\[
11 \sqrt{11} \approx 36.4828726939094
\][/tex]
So, the simplified expression [tex]\( 6 \sqrt{11} + 5 \sqrt{11} \)[/tex] is [tex]\( 11 \sqrt{11} \)[/tex], and its approximate numerical value is 36.4828726939094.
