Simplifying square root expressions worksheet with ten problems.

Let’s solve each problem step by step. These are all about adding or subtracting square roots — but you can only combine terms if they have the same radical part (like √6, √3, etc.). If the radicals are different, you leave them as is.

---

Problem 1:

-5√6 - 2√6

Same radical? Yes → both are √6
Combine coefficients: -5 - 2 = -7
→ -7√6

---

Problem 2:

-3√5 + 2√5

Same radical? Yes → both are √5
Combine: -3 + 2 = -1
→ -√5

---

Problem 3:

-4√3 + 3√3

Same radical? Yes → √3
Combine: -4 + 3 = -1
→ -√3

---

Problem 4:

-3√6 - 4√6

Same radical? Yes → √6
Combine: -3 - 4 = -7
→ -7√6

---

Problem 5:

-4√10 + 5√10

Same radical? Yes → √10
Combine: -4 + 5 = 1
→ √10

---

Problem 6:

-√6 - 2√6

Think of -√6 as -1√6
So: -1 - 2 = -3
→ -3√6

---

Problem 7:

-√7 - 5√7

Again, -√7 = -1√7
-1 - 5 = -6
→ -6√7

---

Problem 8:

-√10 - 5√10

-1 - 5 = -6
→ -6√10

---

Problem 9:

-3√24 - 3√2 + 2√2

First, simplify √24:
√24 = √(4×6) = 4 × √6 = 2√6
So: -3√24 = -3 × 2√6 = -6√6

Now look at the rest: -3√2 + 2√2 → same radical → (-3 + 2)√2 = -√2

So overall: -6√6 - √2
*(Can’t combine further — different radicals)*

---

Problem 10:

-3√45 - √5 + 2√2

Simplify √45:
√45 = √(9×5) = √9 × 5 = 3√5
So: -3√45 = -3 × 3√5 = -9√5

Now expression becomes:
-9√5 - √5 + 2√2

Combine like terms: -9√5 - √5 = -10√5
Then add 2√2 → can’t combine with √5

Final: -10√5 + 2√2

---

## Final Answer:

1) -7√6
2) -√5
3) -√3
4) -7√6
5) √10
6) -3√6
7) -6√7
8) -6√10
9) -6√6 - √2
10) -10√5 + 2√2