What is the approximate value of the square root of 2?

What is the approximate value of the square root of 2?

• A. 1.41
• B. 1.21
• C. 1.61
• D. 2.01

Answer: (A)

The approximate value of the square root of 2 is commonly known to be around 1.41. To understand why this is the case, consider that the square root of a number is the value that, when multiplied by itself, gives that number. For 2, this means we are looking for a number that approximately satisfies the equation x² = 2. When calculating or estimating square roots, knowing the squares of nearby integers helps. The squares of 1 and 2 are 1 and 4, respectively. Since 2 is between these two squares, the square root must be between 1 and 2. More precisely, if we test the decimal 1.4: - 1.4 × 1.4 = 1.96, which is very close to 2. - Testing 1.5 gives 1.5 × 1.5 = 2.25, which is above 2. Therefore, the square root of 2 is indeed closer to 1.4 rather than to 1.5 or any other values presented. Thus, the value of 1.41 is the most accurate estimate of the square root of 2 among the provided choices.

The approximate value of the square root of 2 is commonly known to be around 1.41. To understand why this is the case, consider that the square root of a number is the value that, when multiplied by itself, gives that number. For 2, this means we are looking for a number that approximately satisfies the equation x² = 2.

When calculating or estimating square roots, knowing the squares of nearby integers helps. The squares of 1 and 2 are 1 and 4, respectively. Since 2 is between these two squares, the square root must be between 1 and 2. More precisely, if we test the decimal 1.4:

• 1.4 × 1.4 = 1.96, which is very close to 2.

• Testing 1.5 gives 1.5 × 1.5 = 2.25, which is above 2.

Therefore, the square root of 2 is indeed closer to 1.4 rather than to 1.5 or any other values presented. Thus, the value of 1.41 is the most accurate estimate of the square root of 2 among the provided choices.