Question

simplify (√7 + √8)(√7 + √8)

Answer 1

Answer:

(√7)²+√8²+2×√7×√8

15+2√56

15+4√14

Answer 2

The expression can be written as 15 + 4√14.

Given:

(√7 + √8)(√7 + √8)

To find:

Simplified value

Solution:

We are given,

(√7 + √8)(√7 + √8)

Opening the brackets, we get

= √7(√7 + √8) + √8(√7 + √8)

= √7(√7) + √7(√8) + √8(√7) + √8(√8)

= (√7)² + √56 + √56 + (√8)² [∵ √x × √y = √xy]

= 7 + 2√56 + 8

= 15 + 2√56

Now, √56 can be written as √4 x √14 = 2√14

⇒ 15 + 2√56 = 15 + 4√14

∴ The expression can be written as 15 + 4√14.

SPJ2