tenmarks+note+for+Square+Roots

1、Question: Tell whether the statement is always, sometimes or never true. √a + √b = √ab Correct Answer:To analyze this statement, let us take two examples. 1. a = b = 4 √4 + √4 = √(4 x 4) ? 2 + 2 = √16 ? 4 = 4 The statement is true. 2. a = 9, b = 16 √9 + √16 = √(9 x 16) ? 3 + 4 = √144 ? 7 = 12 ? The statement is false. So, the statement √a + √b = √ab is sometimes true.

2、Question: Tell whether the statement is always, sometimes or never true. a√b + a√b = 2ab Correct Answer:To analyze this statement, let us solve the left side of the equation. a√b + a√b = 2a√b 2a√b will be equal to 2ab only when √b = b. This happens only when b = 0 or b = 1. [√0 = 0, √1 = 1] So, the statement a√b + a√b = 2ab is sometimes true.