Solve (9-c^2)^(1/2)

Question

Simplify the expression

9 - c^{2}

Evaluate

(9 - c^{2})^{\frac{1}{2}}

Solution

9 - c^{2}

Show Solution

c_{1} = - 3, c_{2} = 3

Evaluate

(9 - c^{2})^{\frac{1}{2}}

To find the roots of the expression,set the expression equal to 0

(9 - c^{2})^{\frac{1}{2}} = 0

Find the domain

More Steps

Evaluate

9 - c^{2} \geq 0

Rewrite the expression

- c^{2} \geq - 9

Change the signs on both sides of the inequality and flip the inequality sign

c^{2} \leq 9

Take the 2 -th root on both sides of the inequality

c^{2} \leq 9

Calculate

∣ c ∣ \leq 3

Separate the inequality into 2 possible cases

{c \leq 3 c \geq - 3

Find the intersection

- 3 \leq c \leq 3

(9 - c^{2})^{\frac{1}{2}} = 0, - 3 \leq c \leq 3

Calculate

(9 - c^{2})^{\frac{1}{2}} = 0

The only way a root could be 0 is when the radicand equals 0

9 - c^{2} = 0

Move the constant to the right-hand side and change its sign

- c^{2} = 0 - 9

Removing 0 doesn't change the value,so remove it from the expression

- c^{2} = - 9

Change the signs on both sides of the equation

c^{2} = 9

Take the root of both sides of the equation and remember to use both positive and negative roots

c = \pm 9

Simplify the expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

c = \pm 3

Separate the equation into 2 possible cases

c = 3 c = - 3

Check if the solution is in the defined range

c = 3 c = - 3, - 3 \leq c \leq 3

Find the intersection of the solution and the defined range

c = 3 c = - 3

Solution

c_{1} = - 3, c_{2} = 3

Show Solution