Squaring Square Roots

The square of a single square root is the number inside. For example:

This is because the square root of a number is another number whose square is the given number.

To square a product of a whole number and an irrational square root, you just multiply it by itself and then simplify. For example,

This is sometimes necessary when finding a simplified exact length. For example, to find the exact value of x in the triangle on the right, you apply the Pythagorean Theorem and simplify:

 

toc | return to top | previous page | next page