: Find the prime factorization of the number inside the radical. Step 2: Determine the index of the radical. In this case, the index is two because it is a square root, which means we need two of a kind. Step 3: Move each group of numbers or variables from inside the radical to outside the radical.
"Roots" (or "radicals") are the "opposite" operation of applying exponents; we can "undo" a power with a radical, and we can "undo" a radical with a power. For instance, if we square 2, we get 4, and if we "take the square root of 4", we get 2; if we square 3, we get 9, and if we "take the square root of 9", we get 3. In mathematical notation, the previous sentence means the following:
2^2 = 4,\, \mathrm{ so }\, \sqrt{4\,} = 22
2
=4,so
4
=2
3^2 = 9,\, \mathrm{ so }\, \sqrt{9\,} = 33
2
=9,so
9
=3
The " \sqrt{\color{white}{..}\,}
..
" symbol used above is called the "radical"symbol. (Technically, just the "check mark" part of the symbol is the radical; the line across the top is called the "vinculum".) The expression " \sqrt{9\,}
9
" is read as "root nine", "radical nine", or "the square root of nine".
Answers & Comments
Step-by-step explanation:
: Find the prime factorization of the number inside the radical. Step 2: Determine the index of the radical. In this case, the index is two because it is a square root, which means we need two of a kind. Step 3: Move each group of numbers or variables from inside the radical to outside the radical.
Answer:
Answer:
"Roots" (or "radicals") are the "opposite" operation of applying exponents; we can "undo" a power with a radical, and we can "undo" a radical with a power. For instance, if we square 2, we get 4, and if we "take the square root of 4", we get 2; if we square 3, we get 9, and if we "take the square root of 9", we get 3. In mathematical notation, the previous sentence means the following:
2^2 = 4,\, \mathrm{ so }\, \sqrt{4\,} = 22
2
=4,so
4
=2
3^2 = 9,\, \mathrm{ so }\, \sqrt{9\,} = 33
2
=9,so
9
=3
The " \sqrt{\color{white}{..}\,}
..
" symbol used above is called the "radical"symbol. (Technically, just the "check mark" part of the symbol is the radical; the line across the top is called the "vinculum".) The expression " \sqrt{9\,}
9
" is read as "root nine", "radical nine", or "the square root of nine".
Step-by-step explanation:
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