Answer:
D
Explanation:
When you have a square root of a number, you essentially have to find a number that can be multiplied by itself to be equivalent to the original number.
Take, for example, \sqrt[]{4}. 2 times 2 is 4, meaning that the square root of 4 is 2.
Back to the question.
2\sqrt[]{18} - 5\sqrt[]{32}
First, let's find factors of the numbers that have to be squared.
2\sqrt[]{9 * 2} - 5\sqrt[]{16 * 2}
Neat! It seems like we already have two squares available!
2\sqrt[]{(3 * 3) * 2} - 5\sqrt[]{(4 * 4) * 2}
Square 3 and 4:
2*3\sqrt[]{2} - 5*4\sqrt[]{2}
6\sqrt[]{2} - 20\sqrt[]{2}
-14\sqrt[]{2}, Option C.
Now, onto the second question.
7\sqrt[]{24} + \sqrt[]{90} - 8\sqrt[]{54}
Like the first question, let's find some factors
7\sqrt[]{4 * 6} + \sqrt[]{9 * 10} - 8\sqrt[]{9 * 6}
Aha! Looks like we found a couple more squares!
7\sqrt[]{(2*2) * 6} + \sqrt[]{(3*3) * 10} - 8\sqrt[]{(3*3) * 6}
Square all of them:
7*2\sqrt[]{6} + 3\sqrt[]{10} - 8*3\sqrt[]{6}
14\sqrt[]{6} + 3\sqrt[]{10} - 24\sqrt[]{6}
Note that you can only add numbers with similar leftover roots, so let's do just that:
(14\sqrt[]{6} - 24\sqrt[]{6}) + 3\sqrt[]{10}
-10\sqrt[]{6} + 3\sqrt[]{10}, Option D.