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Cogito

Algebra 2 · Chapter 5 · Lesson 2

Practice Worksheet

Simplifying and Combining Radicals

Pull out the perfect squares, then collect like terms.

12 problems · about 21 minutes · N-RN.A.2, A-SSE.A.2

NameDate

Figure — use these to answer the problems

The square root curve rises quickly then flattens, which is why large roots grow slowly.
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y = 1√x + 0
  • Point(4, 2)
a, coefficient1
Point on the curve4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. √45 = a√5. What is a?

    Answer

  2. Why can √2 + √3 not be combined?

    • They are unlike radicals, the way 2x and 3y are unlike terms.
    • The numbers are too small.

  3. √18 = a√2. What is a?

    Answer

  4. √75 = a√3. What is a?

    Answer

  5. 3√5 + 4√5 = a√5. What is a?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. √2 × √8 equals what number?

    Answer

  2. √(9 + 16) equals what?

    Answer

  3. 6 ÷ √3, rationalised, is a√3. What is a?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Which pairs are like radicals once simplified?

    • √8 and √18
    • √27 and √12
    • √2 and √3
    • √5 and √7
    • Tick every box that applies.

  2. (2 + √3)(2 − √3) equals what number?

    Answer

  3. The Simplify

    √12 simplifies to a√3. What is a?

    Answer

  4. The Diagonal

    A square has area 32. Its side is a√2. What is a?

    Answer