https://file.aiquickdraw.com/mathbot/file/1728874953500r51fh06k.jpg

The given expression is:

\[
5\sqrt{243} + 2\sqrt{27} - \sqrt{75} - 3\sqrt{48}
\]

Let's simplify each square root term:

1. \( \sqrt{243} = \sqrt{81 \times 3} = 9\sqrt{3} \)
2. \( \sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3} \)
3. \( \sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3} \)
4. \( \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} \)

Now substitute these simplified terms back into the expression:

\[
5(9\sqrt{3}) + 2(3\sqrt{3}) - 5\sqrt{3} - 3(4\sqrt{3})
\]

This becomes:

\[
45\sqrt{3} + 6\sqrt{3} - 5\sqrt{3} - 12\sqrt{3}
\]

Now, combine all the terms involving \( \sqrt{3} \):

\[
(45 + 6 - 5 - 12)\sqrt{3} = 34\sqrt{3}
\]

So, the simplified form of the expression is:

\[
34\sqrt{3}
\]

Would you like any further details or clarification?

---

Here are some related questions you might find useful:
1. How do you simplify square roots in general?
2. What is the process for combining like terms in algebraic expressions?
3. Can you simplify an expression like \( \sqrt{72} + \sqrt{50} \)?
4. How do you factor numbers inside a square root to simplify them?
5. How can you apply the distributive property to algebraic terms with radicals?

**Tip:** When simplifying square roots, always look for perfect squares within the number to simplify the expression easily.

Bentuk sederhana dari 5√243 + 2√27 − √75 − 3√48 adalah ....

Learn how to simplify the radical expression 5√243 + 2√27 − √75 − 3√48 by breaking down square roots and combining like terms. This problem involves key algebraic concepts like simplification of radicals and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation