Final answer:
To simplify 7√54 - 2√24, we simplify the square roots first and then combine like terms.
Step-by-step explanation:
To simplify the expression 7√54 - 2√24, we need to simplify the square roots first. We can simplify √54 as 3√6, since 54 can be factored into 9 and 6. Similarly, we can simplify √24 as 2√6, since 24 can be factored into 4 and 6.
Now, we can substitute these simplified square roots back into the expression, giving us 7(3√6) - 2(2√6). Multiplying the coefficients and combining like terms, we get 21√6 - 4√6.
Finally, we can combine the terms with the common square root, resulting in (21 - 4)√6 = 17√6.