Simplify the Following Expressions: (Sqrt3 + Sqrt7)^2 - Mathematics

Simplify the following expressions:

(sqrt3 + sqrt7)^2

Solution

We know that (a + b)^2 = a^2 + b^ + 2ab We will use this property to simplify the expression

(sqrt3 + sqrt7)^2

∴(sqrt3 + sqrt7)^2 = (sqrt3)^2 + (sqrt7)^2 + 2 xx sqrt3 xx sqrt7

= sqrt(3 xx 3) + sqrt(7 xx 7) + 2 xx  sqrt(3 xx 7)

= (3^2)^(1/2) + (7^2)^(1/2) + 2sqrt21

= 3^1+ 7^1 + 2sqrt21

= 10 + 2sqrt21

Hence the value of expression is 10 + 2sqrt21

Concept: Operations on Real Numbers
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.1 | Q 4.1 | Page 3

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