Square roots

The square root shows us which number has been raised to the second power. It is thus an inverse operation of the second power.

The square root of a positive real number a is a positive number b. The number b raised to the second power is a number a. Thus, the square root can only be calculated from a positive number and the result of the square root is always positive.

Square root rules

Example 1

Simplify the square roots below

The first is the number 72 and we divide it by its factors and see whether there are numbers among the factors that give an integer square root.

For the second question, we can use the square root product rule in the other direction and combine the numbers under the same square root.

For the third question, the quotient is combined under the same root

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