Question: Simplify. √8y + √50y Assume that the variable represents a positive real number.

Simplify. √8y + √50y Assume that the variable represents a positive real number.

Solution

To simplify the expression \(\sqrt{8y} + \sqrt{50y}\): First, simplify each square root individually. For \(\sqrt{8y}\): \[ 8y = 4 \times 2y = 2^2 \times 2y \] So, \[ \sqrt{8y} = \sqrt{2^2 \times 2y} = 2\sqrt{2y} \] Next, simplify \(\sqrt{50y}\): \[ 50y = 25 \times 2y = 5^2 \times 2y \] So, \[ \sqrt{50y} = \sqrt{5^2 \times 2y} = 5\sqrt{2y} \] Now, combine the simplified square roots: \[ 2\sqrt{2y} + 5\sqrt{2y} = (2 + 5)\sqrt{2y} = 7\sqrt{2y} \] The simplified form is \(7\sqrt{2y}\).