We read your photo as:

Simplify the square root of 96.

Mathematics

ScanSolve AI Answer

Answer

464\sqrt{6}

Step-by-step solution

4 steps
  1. Find the prime factorization of 96.

    96=2×4896 = 2 \times 48 48=2×2448 = 2 \times 24 24=2×1224 = 2 \times 12 12=2×612 = 2 \times 6 6=2×36 = 2 \times 3

    So, the prime factorization of 96 is 2×2×2×2×2×3=25×32 \times 2 \times 2 \times 2 \times 2 \times 3 = 2^5 \times 3.

  2. Rewrite the square root using the prime factorization.

    96=25×3\sqrt{96} = \sqrt{2^5 \times 3}
  3. Extract any perfect square factors from under the radical.

    We can write 252^5 as 24×22^4 \times 2.

    24×2×3=(22)2×6\sqrt{2^4 \times 2 \times 3} = \sqrt{(2^2)^2 \times 6}
  4. Simplify the expression.

    (22)2×6=(22)2×6\sqrt{(2^2)^2 \times 6} = \sqrt{(2^2)^2} \times \sqrt{6} =22×6= 2^2 \times \sqrt{6} =46= 4\sqrt{6}

    The simplified form of 96\sqrt{96} is:

    464\sqrt{6}
Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp