In the denominator, we have 4 √ 1 0 × √ 1 0 = 4 0, and in the numerator, we can distribute Since the denominator is a single term containing √ 1 0, we are going to want to multiply both the We begin by recalling that rationalizing the denominator means we need to rewrite this fraction with a rational denominator. Simplify 4 √ 1 0 − 3 √ 7 4 √ 1 0 by rationalizing the denominator. Įxample 2: Simplifying a Fraction by Rationalizing the Denominator We multiply the numerator and denominator Where □ is a real number and □ is a positive integer. We can follow this same process to rationalize the denominator of any fraction in the form □ √ □, However, if we rationalize the denominators first, we get an easier way to understand the result:ġ √ 2 + 1 √ 3 = 1 √ 2 × √ 2 √ 2 + 1 √ 3 × √ 3 √ 3 = √ 2 2 + √ 3 3 = 3 √ 2 + 2 √ 3 6. For example, if we want to evaluateġ √ 2 + 1 √ 3, then we can do this by cross multiplication to getġ √ 2 + 1 √ 3 = √ 3 + √ 2 √ 2 × √ 3 = √ 3 + √ 2 √ 6. Thisįorm also allows for easier addition and subtraction of these numbers. For example, 1 √ 2 is the multiplicative inverse of √ 2,īut written in the form √ 2 2, we see it is half the value of √ 2. We often think of this form of number as a simplified form of the radical numbers since it is easier to comprehend the value We can also think of this as multiplying a fraction by √ 2 √ 2 = 1, once again not changing It is worth noting that multiplying the numerator and denominator of a fraction by the same number will not change its value. The real number 1 √ 2 can be rewritten to have a rational denominator by multiplying both its In general, rationalizing the denominator means rewriting a fraction to have a rational number as its denominator. In this explainer, we will learn how to rationalize square roots in the denominators of fractions.
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