Question

x3 with square root of 147 minus 2x square root of 27x4

Answer 1

To simplify the expression \( x^3 \sqrt{147} - 2x \sqrt{27} x^4 \), let's work through it step by step.

1. **Simplify \(\sqrt{147}\)**:
\[
\sqrt{147} = \sqrt{49 \times 3} = \sqrt{49} \cdot \sqrt{3} = 7\sqrt{3}
\]

2. **Simplify \(\sqrt{27}\)**:
\[
\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \cdot \sqrt{3} = 3\sqrt{3}
\]

3. **Substituting back into the expression**:
Now substitute these simplifications back into the original expression:
\[
x^3 \sqrt{147} - 2x \sqrt{27} x^4 = x^3 (7\sqrt{3}) - 2x(3\sqrt{3}) x^4
\]

4. **Distributing and simplifying**:
For the first term,
\[
x^3 (7\sqrt{3}) = 7x^3\sqrt{3}
\]
For the second term,
\[
2x(3\sqrt{3}) x^4 = 6x^5\sqrt{3}
\]

5. **Combining the terms**:
Now, rewrite the entire expression:
\[
7x^3\sqrt{3} - 6x^5\sqrt{3}
\]

6. **Factor out the common term**:
Factor out \(\sqrt{3}\):
\[
\sqrt{3}(7x^3 - 6x^5)
\]

The final simplified expression is:
\[
\sqrt{3}(7x^3 - 6x^5)
\]