Mastering Radical Expressions PRACTICE Quiz

Answer explanation

To simplify \( \sqrt{50} \), we can factor it as \( \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2} \). Thus, the correct answer is \( 5\sqrt{2} \).

Which of the following are like radical terms?

Answer explanation

To add the terms, combine the coefficients of \(\sqrt{5}\): \(3 + 2 = 5\). Thus, \(3\sqrt{5} + 2\sqrt{5} = 5\sqrt{5}\). The correct answer is \(5\sqrt{5}\).

Answer explanation

To subtract the terms, combine like radicals: 7√3 - 2√3 = (7 - 2)√3 = 5√3. Thus, the correct answer is 5√3.

Answer explanation

To multiply the square roots, use the property \( \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \). Here, \( \sqrt{2} \times \sqrt{8} = \sqrt{16} = 4 \). Thus, the correct answer is \( 4 \).

Answer explanation

To simplify 2\sqrt{18}, first simplify \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2}. Then, 2 \cdot 3\sqrt{2} = 6\sqrt{2}. Thus, the correct answer is 6\sqrt{2}.

Answer explanation

To simplify \(\sqrt{72}\), we factor it as \(\sqrt{36 \times 2} = \sqrt{36} \cdot \sqrt{2} = 6\sqrt{2}\). Thus, the simplified form is \(6\sqrt{2}\), which is the correct answer.

Answer explanation

To add the terms, combine the coefficients of \(\sqrt{7}\): \(4 + 3 = 7\). Thus, \(4\sqrt{7} + 3\sqrt{7} = 7\sqrt{7}\). The correct answer is \(7\sqrt{7}\).

Answer explanation

To subtract the terms, combine like radicals: 5√11 - 2√11 = (5 - 2)√11 = 3√11. Thus, the correct answer is 3√11.

Answer explanation

To multiply, use the property \(a\sqrt{b} \times c\sqrt{d} = (a \times c)\sqrt{b \times d}\). Here, \(3 \times 2 = 6\) and \(\sqrt{2} \times \sqrt{3} = \sqrt{6}\). Thus, the result is \(6\sqrt{6}\), which is the correct answer.