Subtract. Write your answer in simplest form.
negative5 radical 3 minus 8 radical147
To perform the subtraction, we first need to simplify \( \sqrt{147} \).
The prime factorization of 147 is:
\[147 = 3 × 49 = 3 × 7^2\]
So \( \sqrt{147} \) can be simplified by taking the square of 7 out of the radical:
\[\sqrt{147} = \sqrt{3 × 7^2} = 7\sqrt{3}\]
Now we rewrite the original expression:
\(-5\sqrt{3} - 8\sqrt{147}\)
Substitute the simplified form of \( \sqrt{147} \) into the expression:
\(-5\sqrt{3} - 8 \cdot 7\sqrt{3}\)
\(-5\sqrt{3} - 56\sqrt{3}\)
Combine like terms by adding the coefficients:
\((-5 - 56)\sqrt{3}\)
\(-61\sqrt{3}\)
So, the simplest form is \(-61\sqrt{3}\).