Predict the result
Estimate the principal square root of thirteen, using a decimal ending in tenths.
Which two whole numbers bracket the root?

Set up the model
Nine and sixteen are perfect squares.
The principal square root of thirteen is between three and four.

Work the example
Three point six squared equals twelve point nine six, which is close to thirteen.
So three point six is a close estimate for the principal square root of thirteen.
The source also accepts three point seven as a close estimate.

Check the result
Now estimate the principal square root of fifty nine, using tenths.
Square a candidate to check it. Take eight seconds to think.
[Eight-second silent pause to work; the answer remains hidden.]
Seven point six squared is fifty seven point seven six.
Seven point seven squared is fifty nine point two nine, close to fifty nine.
Seven point seven is one representative estimate, rather than the only acceptable answer.

Interpret the result
Use the nonnegative principal square root; check a tenths estimate by squaring it.
This section permits close estimates. A nearest tenth example is not an exclusive grading rule.