MORE... to see my other resources for this topic.--Designed for secondary school students, this sheet can be used for work in class or as a homework.It is also excellent for one-to-one tuition. 1/(√5 + √2)    &= \frac{{11 + 4\sqrt 7 }}{{ - 3}} \hfill \\  You can do that by multiplying the numerator and the denominator of this expression by the conjugate of the denominator as follows: \begin{align} \[\begin{array}{l} 4\sqrt {12} = 4\sqrt {4 \times 3} = 8\sqrt 3 \\ 6\sqrt {32} = 6\sqrt {16 \times 2} = 24\sqrt 2 \\ 3\sqrt {48} = 3\sqrt {16 \times 3} =12\sqrt 3 \end{array}, $\boxed{\begin{array}{*{20}{l}} Rationalize the denominators of the following: Solution: In this case, we will use the following identity to rationalize the denominator: $$\left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right) = {a^3} + {b^3}$$. Summary When you encounter a fraction that contains a radical in the denominator, you can eliminate the radical by using a process called rationalizing the denominator. This process is called rationalising the denominator. The denominator contains a radical expression, the square root of 2.Eliminate the radical at the bottom by multiplying by itself which is \sqrt 2 since \sqrt 2 \cdot \sqrt 2 = \sqrt 4 = 2.. &= \frac{{15 + 6\sqrt 3 + 10\sqrt 3 + 12}}{{{{\left( 5 \right)}^2} - {{\left( {2\sqrt 3 } \right)}^2}}} \hfill \\ Examples of How to Rationalize the Denominator. &= \frac{{27}}{{13}} + \frac{{16}}{{13}}\sqrt 3 \hfill \\ (ii) 1/(√7 −√6) Rationalise the denominator in each of the following and hence evaluate by taking √2 = 1.414, √3 = 1.732 and √5 = 2.236 up to three places of decimal. . = (√7 + √6)/(7 − 6) &= 2 - \sqrt 3 \hfill \\ Consider another example: $$\frac{{2 + \sqrt 7 }}{{2 - \sqrt 7 }}$$. For example, we already have used the following identity in the form of multiplying a mixed surd with its conjugate: \[\left( {a + b} \right)\left( {a - b} \right) = {a^2} - {b^2}$, $\left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right) = {a^3} - {b^3}$. He provides courses for Maths and Science at Teachoo. Introduction: Rationalizing the Denominator is a process to move a root (like a square root or cube root) from the bottom of a fraction to the top.We do it because it may help us to solve an equation easily. Find the value of $${x^2} - 8x + 11$$ . By using this website, you agree to our Cookie Policy. Rationalize the denominators of the following: We let We let \begin{align} &a = 2,b = \sqrt{3}\\\Rightarrow &{a^2} = 4,ab = 2\sqrt{3},{b^2} = \sqrt{9} \end{align} To use it, replace square root sign ( √ ) with letter r. Example: to rationalize $\frac{\sqrt{2}-\sqrt{3}}{1-\sqrt{2/3}}$ type r2-r3 for numerator and 1-r(2/3) for denominator. Access answers to Maths RD Sharma Solutions For Class 7 Chapter 4 – Rational Numbers Exercise 4.2. Find the value to three places of decimals of the following. . The sum of two numbers is 7. (iii) 1/(√5 + √2) Thus, = . = (√7 + 2)/((√7)2 − (2)2) ( As (a + b)(a – b) = a2 – b2 ) The multiplication of the denominator by its conjugate results in a whole number (okay, a negative, but the point is that there aren't any radicals): Click hereto get an answer to your question ️ Rationalise the denominator of the following: √(40)√(3) Example 1: Rationalize the denominator {5 \over {\sqrt 2 }}.Simplify further, if needed. For example, to rationalize the denominator of , multiply the fraction by : × = = = . Ex 1.5, 5 One way to understand the least common denominator is to list all whole numbers that are multiples of the two denominators. This browser does not support the video element. = (√7 + √6)/((√7)2 − (√6)2) An Irrational Denominator! Rationalise the denominator of the following expression, simplifying your answer as much as possible. Solution: In this case, we will use the following identity to rationalize the denominator: $$\left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right) = {a^3} + {b^3}$$.    = &\frac{{3 + \sqrt 2  + 3 + \sqrt 3 }}{{ - 16 + 6\sqrt 2 }} \hfill \\  &= \frac{{3 + 2\sqrt 3 }}{{5 - 2\sqrt 3 }} \times \frac{{5 + 2\sqrt 3 }}{{5 + 2\sqrt 3 }} \hfill \\ Example 3: Simplify the surd $$4\sqrt {12} - 6\sqrt {32} - 3\sqrt{{48}}$$ . Our Cookie Policy of any surds from the past 9 years examples rationalize denominator... Rationalize other types of irrational expressions, we can ’ t calculate it and... Integer which is divisible by each denominators of the following: ( i ) 1/√7 need..., to rationalize the denominator should not be irrational! in carrying out rationalization of irrational,... Simplified to 8 plus X squared, all of that over the square root of 2 all numbers. 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rationalise the denominator of the following

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