Questions: Algebra II Sem 2 Apex Learning 2.3.3 Quiz: Adding and Subtracting Radicals Question 7 of 10 Which choice is equivalent to the expression below? sqrt(40) + 8 sqrt(10) + sqrt(90) A. 10 sqrt(10) B. 13 sqrt(10) C. 7 sqrt(10) D. 18 sqrt(10)

Solution Steps

To simplify the expression \(\sqrt{40} + 8\sqrt{10} + \sqrt{90}\), we need to break down each square root into its prime factors and simplify. We look for perfect squares within each radicand to simplify the square roots. After simplifying, we combine like terms.

To simplify \(\sqrt{40}\), we find the largest perfect square factor of 40, which is 4. Thus, \(\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}\).

Similarly, for \(\sqrt{90}\), the largest perfect square factor is 9. Thus, \(\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10}\).

Now, we combine the simplified terms: \[ 2\sqrt{10} + 8\sqrt{10} + 3\sqrt{10} \]

Combine the coefficients of \(\sqrt{10}\): \[ (2 + 8 + 3)\sqrt{10} = 13\sqrt{10} \]

Final Answer