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sqrt75

$\sqrt{75}$

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Evaluate integers raised to positive rational exponents

Full solution

Q.

\sqrt{75}

Identify Number: Identify the number to be square rooted. $\newline$ We need to find the square root of $75$ .
Factor into Primes: Factor $75$ into its prime factors. $\newline$ $75$ can be factored into $3 \times 5 \times 5$ .
Express as Product: Express $75$ as a product of squares and non-squares. $\newline$ $75 = 3 \times (5^2)$ .
Apply Square Root: Apply the square root to both the square and non-square terms. $\sqrt{75} = \sqrt{3 \times (5^2)}$ .
Simplify Square Term: Simplify the square root of the square term. $\sqrt{5^2} = 5$ .
Combine with Non-Square: Combine the square root of the non-square term with the simplified square root. $\sqrt{75} = \sqrt{3} \times 5$ .
Write Final Form: Write the final simplified form. $\newline$ The square root of $75$ simplifies to $5 \times \sqrt{3}$ .

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