Math evaluation of Quotients entailing Radical Expressions

Math testimonial of Quotients entailing Radical expressions 150 150DeborahDeborah 29, 2014December 2, 2014


In stimulate to divide rational expression accurately, distinct rules because that radical expressions deserve to be followed. Some of those rules include the quotient rule, rules because that finding the square root of quotients, and rationalizing the denominator.

You are watching: Square root of 36/49

The Quotient Rule

Suppose the trouble is to advice the square root of 36/49. The trouble can be created in two different ways, one of two people √ (36)/√ (49) or √ (36/49). The square source of 36/49 fixed with the first method is √ (36)/√ (49) or 6/7. The square source of 36/49 resolved with the second method is √ (36/49) or 6/7. This leads to the Quotient Rule, the for any non-negative number A and also any confident number B, the quotient of 2 square roots is the very same whether the square source is taken indigenous the whole ratio or the square root is take away of the numerator and the denominator separately.

Figure 1: The Quotient preeminence in symbol Form


Square roots of Quotients

This dominance is commutative, so the it way the same whether the square roots space taken together in a proportion or take away separately. Sometimes it is simpler to settle the difficulty if the square root of the numerator and also the denominator are considered separately. The way, they have the right to be streamlined using perfect square root if they are available. Suppose the difficulty is to uncover the square source of 18/50. Neither 18 no one 50 room perfect squares, yet the proportion 18/50 deserve to be multiply by 2/2, to give 36/100. The square source of 36 is 6 and also the square root of 100 is 10, to result in a portion of 6/10, which have the right to be more simplified come 3/5. Alternatively, 18 might be factored together 2 times 9 and 50 together 2 times 25, therefore the ratio could be divided by 2/2 come be additional simplified together 3/5.

Rationalizing the Denominator under the Radical Sign

One the the ways to move a radical out of the denominator is to multiply the number through a kind of 1, so the the denominator i do not care a perfect square. Suppose the expression is √ (3/5). If the entire portion is tho under the radical sign, multiply every number through 5/5 so the the new fraction is 15/25 or √ (15)/5.

Figure 2: The procedure of rationalizing the denominator under the radical sign.


Rationalizing the Denominator exterior the Radical Sign

The other way to relocate a radical out of the denominator is to multiply both the numerator and also the denominator for a type of 1 utilizing radicals. Mean that the ratio is 5/√ (3). In bespeak to relocate the radical the end of the denominator, both the numerator and the denominator have the right to be multiplied by a kind of 1 v the radical expression √3/√3 to result in (5√3)/3.

Figure 3: Rationalizing the denominator by making use of radicals, in price form.

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