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Simplify: −60−−−−√

(1 point)
Responses

30i
30 i

2i15−−√
2 i square root of 15

415−−√
4 square root of 15

215−−√

3 answers

To simplify \(-\sqrt{60}\), we can start by breaking it down:

\[ \sqrt{60} = \sqrt{4 \times 15} = \sqrt{4} \cdot \sqrt{15} = 2\sqrt{15} \]

So,

\[ -\sqrt{60} = -2\sqrt{15} \]

Therefore, the simplified form of \(-\sqrt{60}\) is:

\(-2\sqrt{15}\).

Among the responses provided, the correct answer is:

\(\mathbf{-2\sqrt{15}}\) (which does not appear in the listed responses). However, if you meant to check if there was a representation for this, the closest in spirit to your instruction is \(2i15^{-\frac{1}{2}}\) (if interpreted in complex form).

If you need any further assistance, feel free to ask!

that's because the user doesn't know how to type math.
It was supposed to be √−60 = 2i√15

Thank you for the clarification! Yes, you're correct.

To simplify \( \sqrt{-60} \):

  1. Factor out the negative part: \[ \sqrt{-60} = \sqrt{-1 \times 60} = \sqrt{-1} \cdot \sqrt{60} \]

  2. Substitute \( \sqrt{-1} \) with \( i \): \[ \sqrt{-60} = i \cdot \sqrt{60} \]

  3. Now simplify \( \sqrt{60} \): \[ \sqrt{60} = \sqrt{4 \times 15} = \sqrt{4} \cdot \sqrt{15} = 2\sqrt{15} \]

  4. Combine the results: \[ \sqrt{-60} = i \cdot 2\sqrt{15} = 2i\sqrt{15} \]

Therefore, the simplified form is \(\mathbf{2i\sqrt{15}}\). Thank you for your patience, and let me know if there’s anything else you need!