Sure! Let's find the square roots for the given numbers step by step.
(a) [tex]\(\sqrt{81}\)[/tex]:
The number 81 is a perfect square since it can be expressed as the product of the integer 9, i.e., [tex]\(81 = 9 \times 9\)[/tex]. Therefore, the square root of 81 is:
[tex]\[
\sqrt{81} = 9.0
\][/tex]
(b) [tex]\(\sqrt{1}\)[/tex]:
The number 1 is a perfect square since it can be expressed as the product of the integer 1, i.e., [tex]\(1 = 1 \times 1\)[/tex]. Therefore, the square root of 1 is:
[tex]\[
\sqrt{1} = 1.0
\][/tex]
(c) [tex]\(\sqrt{121}\)[/tex]:
The number 121 is a perfect square since it can be expressed as the product of the integer 11, i.e., [tex]\(121 = 11 \times 11\)[/tex]. Therefore, the square root of 121 is:
[tex]\[
\sqrt{121} = 11.0
\][/tex]
(d) [tex]\(\sqrt{0}\)[/tex]:
The number 0 is a special case where it is its own square, i.e., [tex]\(0 = 0 \times 0\)[/tex]. Therefore, the square root of 0 is:
[tex]\[
\sqrt{0} = 0.0
\][/tex]
(e) [tex]\(\sqrt{49}\)[/tex]:
The number 49 is a perfect square since it can be expressed as the product of the integer 7, i.e., [tex]\(49 = 7 \times 7\)[/tex]. Therefore, the square root of 49 is:
[tex]\[
\sqrt{49} = 7.0
\][/tex]
In summary, the square roots are:
- [tex]\(\sqrt{81} = 9.0\)[/tex]
- [tex]\(\sqrt{1} = 1.0\)[/tex]
- [tex]\(\sqrt{121} = 11.0\)[/tex]
- [tex]\(\sqrt{0} = 0.0\)[/tex]
- [tex]\(\sqrt{49} = 7.0\)[/tex]
