Question

The fractions below are possible values of X in the given equations.write the correct fraction inside the box for each equation.

Answer 1

Given:

`\text { a. } x^(2)=(4)/(9)`

`\text { b. } x^(3)=(27)/(64)`

`\text { c. } x^(2)=(81)/(64)`

`\text { d. } x^(3)=(1)/(8)`

To find:

The value of x for each equation.

Solution:

a)
`x^(2)=(4)/(9)`

`x^(2)=(2^2)/(3^2)`

Taking square root on both sides.

`\sqrt{x^(2)}=\sqrt{ (2^2)/(3^2)}`

Square and square roots get canceled.

`x =(2)/(3)`

b)
`x^(3)=(27)/(64)`

`x^(3)=(3^3)/(4^3)`

Taking cube root on both sides.

`\sqrt[3]{x^(3)} =\sqrt[3]{(3^3)/(4^3) }`

cube and cube roots get canceled.

`x=(3)/(4)`

c)
`x^(2)=(81)/(64)`

`x^(2)=(9^2)/(8^2)`

Taking square root on both sides.

`\sqrt{x^(2)}=\sqrt{ (9^2)/(8^2)}`

Square and square roots get canceled.

`x =(9)/(8)`

d)
`x^(3)=(1)/(8)`

`x^(3)=(1^3)/(2^3)`

Taking cube root on both sides.

`\sqrt[3]{x^(3)} =\sqrt[3]{(1^3)/(2^3) }`

cube and cube roots get canceled.

`x=(1)/(2)`