sqrt(7) is irrational because 7 is not a perfect square — no whole number multiplied by itself equals 7. By contrast, sqrt(9) = 3, sqrt(16) = 4, and sqrt(100) = 10 are all perfect squares with exact whole-number square roots.
Question 2 True / False
sqrt(36) = 18, because 36 ÷ 2 = 18.
TTrue
FFalse
Answer: False
sqrt(36) = 6, because 6 × 6 = 36. The square root asks 'what number times itself gives 36?' not 'what is 36 divided by 2?' Dividing by 2 gives half of 36; taking a square root is a completely different operation. You can verify: 18 × 18 = 324, not 36.
Question 3 Short Answer
Without a calculator, estimate sqrt(50) to one decimal place and explain your reasoning.
Think about your answer, then reveal below.
Model answer: Approximately 7.1. Since 7² = 49 and 8² = 64, sqrt(50) falls between 7 and 8. Because 50 is very close to 49, the root is just barely above 7 (the precise value is about 7.07).
The bracketing technique — finding the two consecutive perfect squares on either side — is the standard method for estimating irrational square roots. The closer the number is to the lower perfect square, the closer the root is to the lower whole number.