To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{49}{36}} \)
\( \frac{\sqrt{49}}{\sqrt{36}} \)
\( \frac{\sqrt{7^2}}{\sqrt{6^2}} \)
\( \frac{7}{6} \)
1\(\frac{1}{6}\)

To subtract these radicals together their radicands must be the same:

3\( \sqrt{75} \) - 7\( \sqrt{3} \)
3\( \sqrt{25 \times 3} \) - 7\( \sqrt{3} \)
3\( \sqrt{5^2 \times 3} \) - 7\( \sqrt{3} \)
(3)(5)\( \sqrt{3} \) - 7\( \sqrt{3} \)
15\( \sqrt{3} \) - 7\( \sqrt{3} \)

Now that the radicands are identical, you can subtract them:

The factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 the greatest factor 80 and 76 have in common.

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

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