# Find the Values the Following Correct to Three Places of Decimals, It Being Given that Sqrt2 = 1.4142, Sqrt3 = 1.732, Sqrt5 = 2.2360, Sqrt6 = 2.4495 and Sqrt10 = 3.162 (3 - Sqrt5)/(3 + 2sqrt5) - Mathematics

Find the values the following correct to three places of decimals, it being given that sqrt2 = 1.4142, sqrt3 = 1.732, sqrt5 = 2.2360, sqrt6 = 2.4495 and sqrt10 = 3.162

(3 - sqrt5)/(3 + 2sqrt5)

#### Solution

We know that rationalization factor for 3 + 2sqrt5 is 3 - sqrt5. We will multiply numerator and denominator of the given expression (3 - sqrt5)/(3 + 2sqrt5) by 3 - 2sqrt5 to get

(3 - sqrt5)/(3 + 2sqrt5) xx (3 - 2sqrt5)/(3 - 2sqrt5) = ((3)^2 - 3 xx 2 xx sqrt5 - 3 xx sqrt5 + 2 xx (sqrt5)^2)/((3)^2 - (2sqrt5)^2)

 = (9 - 9sqrt5 + 10)/(9 - 20)

= (19 - 9sqrt5)/(-11)

= (9sqrt5 - 19)/11

Putting the value of sqrt5, we get

(9sqrt5 - 19)/11 = (9(2.236) - 19)/11

= (20.124 - 19)/11

= 1.124/11

= 0.102

Hence the given expression is simplified to 0.102

Concept: Operations on Real Numbers
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 8.1 | Page 15

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