what is the square root of 26 rounded to the nearest hundreth?

The square root of 26, rounded to the nearest hundredth, is 5.10.

You know how to evaluate square roots like √1, √4, √9 because 1, 4, and 9 are perfect squares.

But what about square roots like √2, √3, and √5? The values of these square roots fall between whole numbers, as shown on the number line below.

Example: Approximating to the Nearest Tenth

Approximate √11 to the nearest tenth.

You know from Example 1 that √11 is between 3 and 4.

Make a list of squares of 3.1, 3.2, . . . , 3.9. From the list, you can see that 11 is between 3.32 and 3.42. So, √11 is between 3.3 and 3.4.

Because 11 is closer to 10.89 than to 11.56, √11 is closer to √10.89 = 3.3. So, to the nearest tenth, √11≈ 3.3.

Rounding decimals is very similar to rounding other numbers. If the thousandths place of a decimal is four or less, it is dropped and the hundredths place does not change. For example, rounding 0.843 to the nearest hundredth would give 0.84.

If the thousandths place is five through nine, the hundredths place is increased by one. The decimal 0.846 rounded to the nearest hundredth is 0.85.

Tag: square root