What is the answer to (z-3)^{2/3}=5 ?

The answer to (z-3)^{2/3}=5 is z=5*5^{1/2}+3,z=-5*5^{1/2}+3

Solve for z: (z-3)^{2/3}=5

The solution is z=5*5^{1/2}+3,z=-5*5^{1/2}+3

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(z - 3)^{\frac{2}{3}} = 5

z = 5 \cdot 5^{\frac{1}{2}} + 3, z = - 5 \cdot 5^{\frac{1}{2}} + 3

Decimal Notation

z = 14.18033 \dots, z = - 8.18033 \dots

Solution steps

(z - 3)^{\frac{2}{3}} = 5

Take both sides of the equation to the power of

3 : (z - 3)^{2} = 125

(z - 3)^{2} = 125

Solve

(z - 3)^{2} = 125 : z = 5 \cdot 5^{\frac{1}{2}} + 3, z = - 5 \cdot 5^{\frac{1}{2}} + 3

z = 5 \cdot 5^{\frac{1}{2}} + 3, z = - 5 \cdot 5^{\frac{1}{2}} + 3

Verify Solutions:

z = 5 \cdot 5^{\frac{1}{2}} + 3

True

, z = - 5 \cdot 5^{\frac{1}{2}} + 3

True

The solutions are

z = 5 \cdot 5^{\frac{1}{2}} + 3, z = - 5 \cdot 5^{\frac{1}{2}} + 3

- 2 = x^{\frac{1}{4}}

4 x - 13 = 1

x - 2 = x + 10

x, x^{\frac{2}{3}} = 16

What is the answer to (z-3)^{2/3}=5 ?
The answer to (z-3)^{2/3}=5 is z=5*5^{1/2}+3,z=-5*5^{1/2}+3
Solve for z: (z-3)^{2/3}=5
The solution is z=5*5^{1/2}+3,z=-5*5^{1/2}+3