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Simplify. Remove all perfect squares from inside the square root. sqrt75=

Simplify.\newlineRemove all perfect squares from inside the square root.\newline75=\sqrt{75}=

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Full solution

Q. Simplify.\newlineRemove all perfect squares from inside the square root.\newline75=\sqrt{75}=
  1. Factor 7575 into prime factors: Factor 7575 into its prime factors.\newline7575 can be factored into 3×5×53 \times 5 \times 5.
  2. Identify perfect squares: Identify the perfect squares in the factorization. 5×55 \times 5 is a perfect square because 52=255^2 = 25.
  3. Rewrite using identified perfect square: Rewrite the square root of 7575 using the identified perfect square.75=3×5×5\sqrt{75} = \sqrt{3 \times 5 \times 5}
  4. Simplify by taking out perfect square: Simplify the square root by taking out the perfect square. 3×5×5=3×52\sqrt{3 \times 5 \times 5} = \sqrt{3} \times \sqrt{5^2}
  5. Calculate square root and simplify: Calculate the square root of the perfect square and simplify the expression. 3×52=3×5\sqrt{3} \times \sqrt{5^2} = \sqrt{3} \times 5
  6. Write final simplified form: Write the final simplified form.\newlineThe simplified form is 5⋅35 \cdot \sqrt{3}.

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