In these lessons, we will certainly look in ~ some instances of simplifying fractions in ~ a square source (or radical). Some methods used are: find the square source of the numerator and also denominator separately, minimize the portion and change to not correct fraction.

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### Separate molecule & Denominator

A. The square root of some fractions have the right to be identified by detect the square root of the numerator and also denominator separately.

Example:$$\sqrt \frac1625 = \frac\sqrt 16 \sqrt 25 = \frac\sqrt 4^2 \sqrt 5^2 = \frac45$$

For any type of positive number x and y,$$\sqrt \fracxy = \frac\sqrt x \sqrt y$$

In other words, the square source of a fraction is a portion of square roots.

### Reduce Fraction

B. some fractions can be diminished to fractions through perfect squares as the numerator and also denominator. Then, the square source of the simplified portion can be identified as displayed in the instance below.

Example:$$\sqrt \frac1850 = \sqrt \frac925 = \frac\sqrt 3^2 \sqrt 5^2 = \frac35$$

### Change to Improper Fraction

C. because that a blended number, change it to an improper fraction before finding the square root.

Example:$$\sqrt 1\frac1336 = \sqrt \frac4936 = \frac\sqrt 7^2 \sqrt 6^2 = \frac76 = 1\frac16$$

Example:Calculate the value of every of the following: $$\beginarrayl\rma)\,\,\sqrt \frac2536 \\\rmb)\,\,\sqrt \frac1832 \\\rmc)\,\,\sqrt 1\frac1125 \endarray$$

Solution:

How to leveling fractions inside a square root?

How to leveling square roots in the denominator of a fraction?

Square root of Fractions/Rational Numbers

Finding the square of reasonable numbers for perfect squares and also estimating non-perfect squares.

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Quotient rule & simple Square Roots

An introduction to the quotient rule for square roots and also radicals and how to use it to leveling expressions comprise radicals.

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