Sure, let's find the value of the expression [tex]\((- \sqrt{3})^3 + (\sqrt{2})^2\)[/tex] step-by-step.
1. Calculate [tex]\((- \sqrt{3})^3\)[/tex]:
- First, we find [tex]\(\sqrt{3}\)[/tex]. The square root of 3 is approximately [tex]\(1.732\)[/tex].
- Then, we apply the negative sign: [tex]\(-\sqrt{3} \approx -1.732\)[/tex].
- Next, we raise [tex]\(-1.732\)[/tex] to the power of 3:
[tex]\[
(-1.732)^3 = -1.732 \times -1.732 \times -1.732
\][/tex]
- Multiplying these together, we find the result is approximately [tex]\(-5.196152422706631\)[/tex].
2. Calculate [tex]\((\sqrt{2})^2\)[/tex]:
- First, we find [tex]\(\sqrt{2}\)[/tex]. The square root of 2 is approximately [tex]\(1.414\)[/tex].
- Next, we square [tex]\(1.414\)[/tex]:
[tex]\[
(1.414)^2 = 1.414 \times 1.414
\][/tex]
- Multiplying these together, we get approximately [tex]\(2.0000000000000004\)[/tex].
3. Add the results from the two parts:
- We have the results from the previous calculations:
[tex]\[
(-\sqrt{3})^3 \approx -5.196152422706631
\][/tex]
[tex]\[
(\sqrt{2})^2 \approx 2.0000000000000004
\][/tex]
- Adding these two values together:
[tex]\[
-5.196152422706631 + 2.0000000000000004 \approx -3.1961524227066307
\][/tex]
Therefore, the value of the expression [tex]\((- \sqrt{3})^3 + (\sqrt{2})^2\)[/tex] is approximately [tex]\(-3.1961524227066307\)[/tex].
