# Find the Value to Three Places of Decimals of the Following. It is Given that Sqrt2 = 1.414, Sqrt3 = 1.732, Sqrt5 = 2.236 and Sqrt10 = 3.162 (Sqrt10 + Sqrt15)/Sqrt2 - Mathematics

Find the value to three places of decimals of the following. It is given that

sqrt2 = 1.414, sqrt3 = 1.732, sqrt5 = 2.236 and sqrt10 = 3.162

(sqrt10 + sqrt15)/sqrt2



#### Solution

We know that rationalization factor of the denominator is sqrt2. We will multiply numerator and denominator of the given expression (sqrt10 + sqrt15)/sqrt2 by sqrt2 to get

(sqrt10 + sqrt15)/sqrt2 xx sqrt2/sqrt2 = (sqrt10 xx sqrt2 + sqrt15 xx sqrt2)/(sqrt2 xx sqrt2)

= (sqrt10 xx sqrt2 + sqrt5 xx sqrt3 xx sqrt2)/2

= (3.162 xx 1.414 + 2.236 xx 1.732 xx 1.414)/2

= 9.947/2`

= 4.9746

The value of expression 4.9746 can  be round off to three decimal places as 4.975.

Hence the given expression is simplified to 4.975

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

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 2.4 | Page 14

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