Combine like radical terms -7\sqrt(6-5 ) \sqrt(54)
-7√(6-5)√(54) = -7(√1)(3√6) = -21√6
I suspect a typo...
To combine like radical terms, we first simplify each radical term, if possible. Let's start by simplifying the expression -7\sqrt{6-5}:
The term \sqrt{6-5} can be simplified to \sqrt{1}, which is equal to 1. Therefore, -7\sqrt{6-5} can be simplified to -7(1) or simply -7.
Now, let's simplify the expression \sqrt{54}:
We can factor 54 as 9 * 6. Since 9 is a perfect square (3^2 = 9), we can simplify the expression \sqrt{54} as \sqrt{9}\sqrt{6}. The square root of 9 is 3, so the expression becomes 3\sqrt{6}.
Now that we have simplified both radical terms, we can combine them:
-7 + 3\sqrt{6}
Therefore, the combined like radical terms of -7\sqrt{6-5} and \sqrt{54} is -7 + 3\sqrt{6}.
To combine like radical terms, you need to simplify each radical term separately and then add or subtract them.
Let's start by simplifying each radical term step by step:
1. Simplify the first radical term: -7√(6-5)
Since there is no square root inside the parentheses, we can distribute the -7 to each term within the parentheses:
-7√(6) + 7√(5)
2. Simplify the second radical term: √(54)
Firstly, identify any perfect square factors of 54.
The perfect square factors of 54 are 9 (3^2) and 6 (2^2 * 3).
Rewrite 54 as the product of these factors:
√(9 * 6)
Next, split the square root into separate square roots:
= √(9) * √(6)
Evaluate the square root of 9:
= 3 * √(6)
Now, we have simplified both radical terms:
-7√(6) + 7√(5) + 3√(6)
To combine like radical terms, we look for radicals with the same radicand (the expression inside the square root symbol). In this case, we have √(6) in both terms.
Combine the coefficients of the like radical terms (the numbers in front of the square root symbol):
-7√(6) + 3√(6)
Finally, -7√(6) + 3√(6) can be further simplified as -4√(6).