Question

Approximate pi plus the square root of 70 to the nearest hundredth.

8.37
11.14
11.51
12.14

Answer 1

Explanation:

√70 = 8.37(correct to the nearest hundredth(CTTNH))

π = 3.14(CTTNH)

8.37+3.14=11.51

Answer 2

11.51

Explanation:

Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, ...

To approximate the square root of a number, find the perfect squares immediately before and after the given number.

The perfect squares immediately before and after 70 are 64 and 81.

Therefore:

⇒ 64 < 70 < 81

⇒ √64 < √70 < √81

⇒ 8 < √70 < 9

Therefore, √70 is between 8 and 9.

We know that π ≈ 3.14.

⇒ 8 + 3.14 = 11.14

⇒ 9 + 3.14 = 12.14

Therefore:

11.14 < √70 + π < 12.14

As 70 is closer to 64 than 81, √70 will be closer to 8 than 9.

Therefore, π + √70 ≈ 11.51.