Questions: Add the radical expressions. 5 sqrt(96)+3 sqrt(150)= sqrt()

Solution Steps

To add the radical expressions, first simplify each square root by factoring out perfect squares. Then, combine like terms if possible.

We start by simplifying the radicals in the expression \( 5 \sqrt{96} + 3 \sqrt{150} \).

For \( \sqrt{96} \): \[ \sqrt{96} = \sqrt{16 \cdot 6} = \sqrt{16} \cdot \sqrt{6} = 4\sqrt{6} \]

For \( \sqrt{150} \): \[ \sqrt{150} = \sqrt{25 \cdot 6} = \sqrt{25} \cdot \sqrt{6} = 5\sqrt{6} \]

Now we can rewrite the original expression using the simplified radicals: \[ 5 \sqrt{96} + 3 \sqrt{150} = 5(4\sqrt{6}) + 3(5\sqrt{6}) = 20\sqrt{6} + 15\sqrt{6} \]

Next, we combine the like terms: \[ 20\sqrt{6} + 15\sqrt{6} = (20 + 15)\sqrt{6} = 35\sqrt{6} \]

To find the numerical value of \( 35\sqrt{6} \): \[ \sqrt{6} \approx 2.4495 \quad \Rightarrow \quad 35\sqrt{6} \approx 35 \times 2.4495 \approx 85.7321 \]

Final Answer