Given:
[tex]\text { a. } x^{2}=\frac{4}{9}[/tex]
[tex]\text { b. } x^{3}=\frac{27}{64}[/tex]
[tex]\text { c. } x^{2}=\frac{81}{64}[/tex]
[tex]\text { d. } x^{3}=\frac{1}{8}[/tex]
To find:
The value of x for each equation.
Solution:
a) [tex]x^{2}=\frac{4}{9}[/tex]
[tex]x^{2}=\frac{2^2}{3^2}[/tex]
Taking square root on both sides.
[tex]\sqrt{x^{2}}=\sqrt{ \frac{2^2}{3^2}}[/tex]
Square and square roots get canceled.
[tex]x =\frac{2}{3}[/tex]
b) [tex]x^{3}=\frac{27}{64}[/tex]
[tex]x^{3}=\frac{3^3}{4^3}[/tex]
Taking cube root on both sides.
[tex]\sqrt[3]{x^{3}} =\sqrt[3]{\frac{3^3}{4^3} }[/tex]
cube and cube roots get canceled.
[tex]x=\frac{3}{4}[/tex]
c) [tex]x^{2}=\frac{81}{64}[/tex]
[tex]x^{2}=\frac{9^2}{8^2}[/tex]
Taking square root on both sides.
[tex]\sqrt{x^{2}}=\sqrt{ \frac{9^2}{8^2}}[/tex]
Square and square roots get canceled.
[tex]x =\frac{9}{8}[/tex]
d) [tex]x^{3}=\frac{1}{8}[/tex]
[tex]x^{3}=\frac{1^3}{2^3}[/tex]
Taking cube root on both sides.
[tex]\sqrt[3]{x^{3}} =\sqrt[3]{\frac{1^3}{2^3} }[/tex]
cube and cube roots get canceled.
[tex]x=\frac{1}{2}[/tex]
