Finding Square Roots
To find the square root of a perfect square, think of what number times itself
is equal to the perfect square. Look at the square root of twenty-five. What
factor times itself is equal to twenty-five? Five times five equals twenty-five. So,
the square root of twenty-five equals five.
Try another example. Find the square root of one hundred forty-four. What
factor times itself is equal to one hundred forty-four? Twelve times twelve
equals one hundred forty-four. So, the square root of one hundred forty-four
equals twelve.
To find the square root of a number with a decimal, think of the number
without the decimal. Then, add a decimal to the factors. If there are two decimal
places in the perfect square, then there should be two decimal places in the
factors. Look at the number one and twenty-one hundredths. First, think of the
number without the decimal. The number without the decimal is one hundred
twenty-one. You know that eleven times eleven equals one hundred twenty-one.
Look at the original number and add decimal points to the factors. Remember,
you always want to have the same number of place values in all numbers. So,
eleven becomes one and ten hundredths. The square root of one and twenty-one
hundredths is one and ten-hundredths.
What if the square root is negative? Simply think of what number times
itself is equal to the perfect square and then just add a negative. To find the
square root of the negative of forty-nine, determine what factor times itself is
equal to forty-nine. Seven times seven equals forty-nine, so the square root of
forty-nine is seven. Since there was a negative in front of the square root sign,
we need to add a negative the answer. The correct answer is negative seven.
Sometimes you are asked to find the root of numbers that are not perfect
squares. In that case, you can estimate the correct answer. For example, eight is
not a perfect square. But you know that the square root of four is two and the
square root of nine is three. So, the square root of eight is between two and three.
Since is eight is closer to nine, you can estimate that the square root of eight is
about three.
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