To simplify the square root expressions, we need to understand the simplification process of each square root and then put them together. Here is the detailed step-by-step solution:
1. Simplify [tex]\( \sqrt{63} \)[/tex]:
- Note that 63 can be factored into 9 and 7: [tex]\( 63 = 9 \times 7 \)[/tex].
- Take the square root of each factor: [tex]\( \sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} \)[/tex].
- We know [tex]\( \sqrt{9} = 3 \)[/tex], so [tex]\( \sqrt{63} = 3\sqrt{7} \)[/tex].
2. Simplify [tex]\( \sqrt{1} \)[/tex]:
- The number 1 is a perfect square, so [tex]\( \sqrt{1} = 1 \)[/tex].
3. Combining the simplifications:
- We already simplified [tex]\( \sqrt{63} \)[/tex] to [tex]\( 3\sqrt{7} \)[/tex] and [tex]\( \sqrt{1} \)[/tex] to 1. We then combine them.
Therefore, the simplified form of [tex]\( \sqrt{63} \)[/tex] and [tex]\( \sqrt{1} \)[/tex] is:
[tex]\( 3\sqrt{7} \)[/tex] and 1 respectively.
So the simplified form when combined is:
[tex]\[ 3\sqrt{7} \sqrt{1} = 3\sqrt{7} \cdot 1 = 3\sqrt{7} \][/tex]
Select the correct answer from each drop-down menu.
Simplify.
[tex]$
\sqrt{63}
$[/tex]
[tex]\[3\sqrt{7}\][/tex]
[tex]$\sqrt{1}$[/tex]
[tex]\[1\][/tex]
Therefore,
[tex]$
\sqrt{63} \cdot \sqrt{1} = 3\sqrt{7}
$[/tex]
