Respuesta :
Given:
Consider the expression are
1) [tex]\sqrt{36}[/tex]
2) [tex]\sqrt[3]{-8}[/tex]
3) [tex]-\sqrt{100}[/tex]
4) [tex]\sqrt[3]{27}[/tex]
To find:
The simplified form of each expression.
Solution:
1. We have,
[tex]\sqrt{36}=\sqrt{6^2}[/tex]
[tex]\sqrt{36}=6[/tex]
Therefore, the value of this expression is 6.
2. We have,
[tex]\sqrt[3]{-8}=(-8)^{\frac{1}{3}}[/tex]
[tex]\sqrt[3]{-8}=((-2)^3)^{\frac{1}{3}}[/tex]
[tex]\sqrt[3]{-8}=(-2)^{\frac{3}{3}}[/tex]
[tex]\sqrt[3]{-8}=-2[/tex]
Therefore, the value of this expression is -2.
3. We have,
[tex]-\sqrt{100}=-\sqrt{10^2}[/tex]
[tex]-\sqrt{100}=-10[/tex]
Therefore, the value of this expression is -10.
4. We have,
[tex]\sqrt[3]{27}=(27)^{\frac{1}{3}}[/tex]
[tex]\sqrt[3]{27}=(3^3)^{\frac{1}{3}}[/tex]
[tex]\sqrt[3]{27}=(3)^{\frac{3}{3}}[/tex]
[tex]\sqrt[3]{27}=3[/tex]
Therefore, the value of this expression is 3.
