# Simplifying Square Roots

A square root of a number is one of two equal factors of the number. A radical sign, , is used to indicate a positive square root.

Every positive number has a positive square root and a negative square root. A negative number like –4 has no real square root because the square of a number cannot be negative.

Example:

Find the square root.

indicates the positive square root of 49.

Since 7 × 7 is 49, = 7.

Find the square root.

indicates the negative square root of 25.

Since 5 × 5 is 25, = –5 .

Estimate Square Root

The square root of a perfect square is an integer. You can estimate the square root of a number that is not a perfect square.

Example:

Estimate to the nearest whole number.

First list some perfect squares and look for the whole numbers near by 69.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, …

Observe that 69 lies between the perfect squares 64 and 81. That is, 64 < 69 < 81.

Now find the square root of each number.

So, is between 8 and 9.

Since 69 is much closer to 64 than to 81, the best whole number estimate is 8.