Question

Simplify :- (2√5+3√5)²
Please tell me the answere as faster as you can . and tell me in fully explanation .
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Answer 1

Step-by-step explanation:

(2√5+3√5)² = (5√5)²

(5√5) (5√5)= 25×5=125

Answer 2

Answer:

(√3+√5)²

Step-by-step explanation:

Let us assume to the contrary that (√3+√5)² is a rational number,then there exists a and b co-prime integers such that,

(√3+√5)²=a/b

3+5+2√15=a/b

8+2√15=a/b

2√15=(a/b)-8

2√15=(a-8b)/b

√15=(a-8b)/2b

(a-8b)/2b is a rational number.

Then √15 is also a rational number

But as we know √15 is an irrational number.

This is a contradiction.

This contradiction has arisen as our assumption is wrong.

Hence (√3+√5)² is an irrational number.