### Concept (1)

When a radical is not a perfect square (1, 4, 9, 16, ), estimating square roots is a valuable tool. When asked to estimate the value of a radical between two consecutive integers, find the two perfect squares that are slightly less and slightly more than the radicand. Also, remember that negative numbers do not have a real number square root.

### Sample Problems (8)

Need help with "Completing the Square" problems? Watch expert teachers solve similar problems to develop your skills.

Solve:

3p² − 12p − 15 = 0
###### Problem 1
How to make a binomial into a perfect square trinomial.

Solve x² − 10x − 40 = 0 by completing the square. Round your answer to the nearest hundredth.

###### Problem 2
How to complete the square when the a term is not equal to 1.

Solve 4x² − 4x + 9 = 0 by completing the square.

###### Problem 3
How to complete the square when there are fractional solutions.

Make x² + 8x + ___ a perfect square trinomial.

###### Problem 4
How to use completing the square to recognize a quadratic equation with no solutions.
###### Problem 5
Finding the third term (c) that completes a perfect square trinomial.
###### Problem 6
How to complete the square when "a" is one and "b" is odd.
###### Problem 7
Solving a quadratic equation by completing the square when "a" is one and "b" is even.
###### Problem 8
Using algebra tiles to demonstrate completing the square.