find the square root of 2.2 correct to two place of decimal

find the square root of 2.2 correct to two place of decimal

The correct answer and explanation is:

Correct Answer:
The square root of 2.2, correct to two decimal places, is 1.48.

Explanation (300 words):

To find the square root of a number like 2.2 to two decimal places, we are essentially looking for a number which, when multiplied by itself, gives us a value as close as possible to 2.2.

We can use either:

1. A calculator, or
2. A method like trial and error or the long division method.

Step-by-step (Trial and Error Method)

We begin by identifying two perfect squares near 2.2:

• √1 = 1
• √4 = 2
  So √2.2 is between 1 and 2.

Try squaring some values between 1 and 2:

• 1.4² = 1.96
• 1.5² = 2.25
  So √2.2 is between 1.4 and 1.5.

Now, narrow it down:

• 1.47² = 2.1609
• 1.48² = 2.1904
• 1.49² = 2.2201

Now observe:

• 1.48² = 2.1904 (very close to 2.2)
• 1.49² = 2.2201 (slightly over 2.2)

So √2.2 ≈ 1.48 is a better estimate than 1.49.

Using a Calculator

Typing “√2.2” into a calculator gives 1.4832…
When we round 1.4832 to two decimal places, we get 1.48.

Summary

The square root of 2.2 lies between 1 and 2, more precisely between 1.47 and 1.49. When computed using a calculator or approximation, the result is 1.48 (rounded to 2 decimal places). This is useful in math, science, and engineering for approximating non-perfect square roots.