Use the square root property to determine all real solutions for each of the following equations. \( 5 c^{2}-60=0 \) \( c=\square \) \( 48^{2}+48=0 \) \( 8=\square \) Give exact solutions (don't use decimals), and separate multiple solutions with commas. If there are no real solutions, type DNE.

To solve the equation \( 5 c^{2}-60=0 \), we can first isolate the \( c^{2} \) term: 1. Add 60 to both sides: \( 5 c^{2} = 60 \) 2. Divide by 5: \( c^{2} = 12 \) 3. Now, apply the square root property: \( c = \pm \sqrt{12} \) which simplifies to \( c = \pm 2\sqrt{3} \). Final solutions: \( c = 2\sqrt{3}, -2\sqrt{3} \). For the equation \( 48^{2}+48=0 \), this is a standard quadratic in the form of \( ax^2 + bx + c \): 1. Apply the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \): here \( a = 48, b = 1, c = 0 \). 2. Compute the discriminant: \( b^2 - 4ac = 1^2 - 4*48*0 = 1 \). 3. Calculate the roots: \( x = \frac{-1 \pm \sqrt{1}}{2*48} \) results in \( x = \frac{-1 \pm 1}{96} \). Thus we have: \( x = 0 \) or \( x = -\frac{1}{96} \). Final solutions: \( 8 = 0, -\frac{1}{96} \).