22/25 In simplest radical form, -5sqrt (75) is equivalent to: -15sqrt (5) 5sqrt (3) -25sqrt (3)

To simplify the expression \(-5\sqrt{75}\), we need to break down the number 75 into its prime factors.<br /><br />First, let's factorize 75:<br />\[ 75 = 3 \times 25 \]<br />\[ 25 = 5 \times 5 \]<br /><br />So, the prime factorization of 75 is:<br />\[ 75 = 3 \times 5^2 \]<br /><br />Now, we can rewrite the expression \(-5\sqrt{75}\) using the prime factorization:<br />\[ -5\sqrt{75} = -5\sqrt{3 \times 5^2} \]<br /><br />We can use the property of square roots that \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\):<br />\[ -5\sqrt{3 \times 5^2} = -5\sqrt{3} \times \sqrt{5^2} \]<br /><br />Since \(\sqrt{5^2} = 5\), we have:<br />\[ -5\sqrt{3} \times \sqrt{5^2} = -5\sqrt{3} \times 5 \]<br /><br />Multiplying the constants, we get:<br />\[ -5 \times 5 \sqrt{3} = -25\sqrt{3} \]<br /><br />Therefore, the expression \(-5\sqrt{75}\) simplifies to:<br />\[ -25\sqrt{3} \]<br /><br />So, the correct answer is:<br />\[ -25\sqrt{3} \]