10MAX Surds Operations Quiz

Answer explanation

Choose the answer that simplifies the surd correctly. In this case, the correct choice is 5√2 as √50 = √(25*2) = 5√2.

Answer explanation

To simplify \(\sqrt{18}\), we can rewrite it as \(\sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3 \times \sqrt{2} = 3\sqrt{2}\), so the correct choice is \(3\sqrt{2}\).

Answer explanation

To add surds, combine like terms. Here, sqrt{8} + sqrt{2} = 2sqrt{2} + sqrt{2} = 3sqrt{2}. Therefore, the correct answer is 3sqrt{2}.

Answer explanation

To subtract surds, simplify each surd first. √27 = √(9*3) = 3√3. √3 remains as is. Subtract to get 3√3 - √3 = 2√3.

Answer explanation

When multiplying surds, you multiply the numbers outside the square root and then multiply the numbers inside the square root. So, \(\sqrt{3} \times \sqrt{12} = \sqrt{3 \times 12} = \sqrt{36} = 6\).

Answer explanation

To divide surds, divide the numbers inside the square roots. \(\frac{\sqrt{50}}{\sqrt{2}} = \sqrt{\frac{50}{2}} = \sqrt{25} = 5\). Therefore, the answer is 5.

Answer explanation

The surd of sqrt(72) simplifies to 6*sqrt(2) by breaking down 72 into 36*2 and taking the square root of 36.

Answer explanation

To add surds, combine like terms. Here, 2√3 and 3√3 are like terms, so add the coefficients: 2 + 3 = 5. The answer is 5√3.

Answer explanation

To subtract surds, combine like terms. Here, 5√7 - 2√7 = 3√7. Therefore, the correct answer is 3√7.

Answer explanation

To multiply surds, multiply the numbers outside the square root and then multiply the numbers inside the square root. \(\sqrt{5} \times \sqrt{20} = \sqrt{5 \times 20} = \sqrt{100} = 10\). Therefore, the answer is 10.