To simplify [tex]\(\sqrt{63}\)[/tex], follow these detailed steps:
1. Factorize the number under the square root: We need to express 63 as a product of its factors. Notice that 63 can be factored into 9 and 7:
[tex]\[
63 = 9 \times 7
\][/tex]
2. Break up the square root: Using the property of square roots that [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex], we can write:
[tex]\[
\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7}
\][/tex]
3. Simplify the square root of the perfect square: The square root of 9 is 3, since [tex]\(3 \times 3 = 9\)[/tex]:
[tex]\[
\sqrt{9} = 3
\][/tex]
4. Combine the results: Now, we multiply the simplified square root of 9 (which is 3) by [tex]\(\sqrt{7}\)[/tex]:
[tex]\[
\sqrt{63} = 3 \times \sqrt{7}
\][/tex]
Thus, the simplified form of [tex]\(\sqrt{63}\)[/tex] is:
[tex]\[
\boxed{3 \times \sqrt{7}}
\][/tex]
You can now select "3" in the first drop-down menu and "[tex]\(\sqrt{7}\)[/tex]" in the second drop-down menu to get the correct simplified result of [tex]\(\sqrt{63}\)[/tex].
